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I. General Considerations
A. Change in Trend. Due to recent difficult economic times and the general unavailability of third-party financing, the business acquisition arena continues to be generally a buyer's market. Accordingly, generally speaking, the buyer with financial resources enjoys substantially increased leverage in structuring the acquisition and the contents of the legal instruments documenting the transaction. In that type of market, the buyer is often able to successfully negotiate one or more basic business points such as a relatively favorable purchase price, low down payment, substantial deferred payments of the purchase price which are seller financed and no personal guarantee of the deferred payments of the purchase price. In addition, oftentimes the deferred payments are based on contingencies, the most common of which are based on future productivity of the purchased business, sometimes referred to as an "earnout" contingency.
B. Negotiation Process. In a typical acquisition involving an attorney, the buyer will generally perform an extensive due diligence review of the company to be purchased and have prepared significant legal documents, usually in the form of an asset purchase agreement, stock purchase agreement or a merger or conversion agreement, along with numerous exhibits and related agreements, such as covenants not to compete, promissory notes, security agreements, consulting or employment agreements and various due diligence and closing certificates of representatives of both buyer and seller. The due diligence and document preparation process not only entails a significant expenditure of both the buyer's and seller's time, emotion and energy, but also, the incurrence of significant expenses in the form of professional fees and related expenses. It is, therefore, imperative that both parties ascertain that there is a "real deal" at the earliest stage possible, so that a party to the transaction is not placed in the position of making unnecessary concessions in order to avoid losing his considerable investment in terms of time and money, which is growing more and more significant as the acquisition process continues.
Worst yet is the exposure of losing the entire deal at the tail end of the due diligence process, due to the inability of the parties to reach agreement on some material point, which point could have often been resolved prior to the expenditure of substantial time and money in the acquisition process. Although negotiation of some points in the later stage of the transaction is almost always unavoidable, the preparation of the definitive agreements should be almost anti-climatic. The most significant negotiation stage of the business acquisition should be consummated at the beginning of the negotiation process and is best documented through a preliminary document often referred to as a letter of intent. Oftentimes, not enough attention is placed on this important document and, too often, it is omitted in its entirety.
II. Letter of Intent
A. From Buyer's Perspective. The letter of intent should clearly outline all major business points, which could be "deal breakers", including, aside from the obvious amount and payment terms of the purchase price, (i) whether any personal guarantees are to be required of the buyer; (ii) whether any assets of the purchased business or other assets of the buyer are to be used as collateral by the seller; (iii) the contents of warranties and representations and the consequences of any violation of any warranties and representations, including whether a right of offset will be granted; (iv) a long survival period for the seller's warranties and representations after closing; (v) whether legal opinions will be required; (vi) the establishment of contingencies on deferred payments, including the parameters of any "earnout" provision; and (vii) restrictions on seller conduct pending the closing process.
B. From Seller's Perspective. Aside from the obvious amount and payment terms of the purchase price, the seller will want (i) personal guarantees of solvent individuals or entities associated with the buyer for any deferred payments; (ii) a security interest in some or all of the purchased assets of the business or in other collateral of the buyer to secure payment of any deferred payments; (iii) specific and short term dates for each step of the closing process, with required earnest money deposits at each stage; (iv) confidentiality provisions; (v) provision for a "deal-breakup" fee; (vi) specific delineation of employment or consulting agreement terms; (vii) provision for "reduced" warranties and representations of seller; (viii) a high "basket" amount before indemnification for breach of seller's warranties and representations would apply; (ix) an appropriate "ceiling" for which the indemnification obligation for breach of seller's warranties and representations cannot exceed; (x) a short survival period for the seller's warranties and representations after closing; and (xi) removal or restriction of contingencies on deferred payments.
III. Personality Styles.
A. Introductory Comments. Accurately identifying a person's personality style ("identification") and then adapting your behaviors to pace the person's personality style ("pacing") is important, not only in life, but in also becoming a skillful negotiator. Skillful negotiators know how to align the differing positions of the parties involved (based on the parties' differing personality styles) with their commonality of interest (in this case, consummating the transaction being negotiated). A fuller discussion of personality styles is beyond the scope of this writing; however, the following is a very brief summary of the nine personality types based on the system used by this author known as the Personagram®.
B. The Assertive Types.
1. The Dominating Challengers*. Seeking autonomy through domination of the environment. The tough boss type. Under stress, become confrontational and threatening. Turn them into the Empowering Challengers*.
2. The Competitive Achievers*. Seeking attention through promotion of an image of success. The executive type, the top salesperson or producer. Under stress, become hostile, usually displaying arrogance and contempt. Turn them into the Authentic Achievers*.
3. The Scattered Enthusiasts*. Seeking security through frenzied activity and excitement. The fun, party type. Under stress, become impatient and pushy. Turn them into the Invigorating Enthusiasts*.
C. The Withdrawn Types.
1. The Stonewalling Peacemakers*. Seeking autonomy through withdrawal and non-confrontation. The pleasant type. Under stress, become stubborn and resigned. Turn them into the Receptive Peacemakers*.
2. The Moody Individualists*. Seeking attention through dramatic withdrawal. The artistic type. Under stress, become overly sensitive and temperamental before withdrawing. Turn them into the Creative Individualists*.
3. The Impractical Investigators*. Seeking security through mastery of critical information. The inventive type (computers, scientists). Under stress, become cynical and argumentative. Turn them into the Inventive Investigators*.
D. The Service Types.
1. The Inflexible Reformers*. Seeking autonomy by being right and without reproach. The perfectionist type. Servicing others unemotionally through reason and logic. Under stress, become inflexible and condescending. Turn them into the Discerning Reformers*.
2. The Meddling Helpers*. Seeking attention through servicing others through emotional support, but expecting a payback. The smothering, mothering type. Under stress, become manipulating (through guilt) and intrusive. Turn them into the Supportive Helpers*.
3. The Negative Loyalists*. Seeking security through strategic alliances (strength in numbers). Servicing others to build alliances. Lacking inner support and guidance. Under stress, create in and out groups, incite others against the "enemy". Turn them into the Dedicated Loyalists*.
* Copy write names of The Personagram Institute, Inc. based on the works of unrelated individuals, Don Richard Riso and Russ Hudson, authors of Personality Types and the Wisdom of the Enneagram. Reprinted with permission.
IV. Negotiation Strategies and Tactics.
A. Avoid Issue Isolation. Never narrow negotiations down to just one issue, as this creates a situation where generally one party must "win" and the other party must "lose." (Dominating Challengers, Competitive Achievers). Leave room for compromise.
B. The Extra Concession. After supposedly reaching agreement on all business points, a party requests an additional, usually small, concession (sometimes called the "nibble"), which was not previously discussed. This tactic is often successful because the other party is feeling good about the agreement at the time and, if such concession were brought up earlier in the negotiation process, it could be eliminated by the other party through the "trade-off" aspect of normal negotiations. (Competitive Achievers, Negative Loyalists, Dominating Challengers). Combat this tactic by making the requesting party feel guilty about his request by stressing what a good deal he has already negotiated.
C. The Hot Potato. One party attempts to transfer its problem (usually not a "real" problem; usually limited budget) to the other party. This tactic is often successful, as the other party psychologically takes ownership of the problem by limiting their activities (staying in budget) or spending resources trying to solve the other party's problem, and the first party has received concessions as a result thereof. (Negative Loyalists). Combat this tactic by immediately testing the validity of the problem and rendering it into a non-problem immediately. (If I find the perfect software program for you for a little more than your budget, would you purchase it or should I only show it to my other customers?)
D. Higher Authority. A party that really has the authority to make a decision pretends that he needs to seek approval from another individual or a group of individuals, thus, setting up the ability to achieve concessions at the next meeting. (Negative Loyalists). Combat this tactic by asking at the beginning of the negotiation process who has authority to decide. The lawyers are often used as the "higher authority", when the clients are talking to each other and the "clients" are often uses as the "higher authority" when the lawyers are talking to each other.
E. Set-Aside Technique. Set-aside controversial issues to avoid impasse and first resolve non-controversial issues to build a foundation of consensus that will enable the parties to later agree on the issues previously set aside. (Effective with Negative Loyalists).
F. Good Guy, Bad Guy. One party will have a "good guy" representative and a "bad guy" representative to build a rapport between the other party and the "good guy" representative. Often used in conjunction with the higher authority tactic. Combat this tactic by recognizing it for what it is and confronting the participants with your knowledge of it.
G. Flinching. A physical or emotional response to a proposal (the "flinch") can be very effective. Oftentimes seen as a physical shudder, look of disgust or fright and followed by a statement such as "That's outrageous!" (Competitive Achievers, Negative Loyalists, Dominating Challengers). If the proposal is sound and reasonable, combat the flinch by staying firm on your proposal.
H. The Withdrawn Offer. When the negotiation process is going too long and the other party appears to be attempting to get that "last" minor concession, an often successful technique can be to withdraw your last offer. (Dominating Challengers). This can often be accomplished, without losing face, by using the "higher authority" technique. The other party will oftentimes retreat back to your last offer.
I. The Red Herring. Some parties often throw in one or more requirements that are not really important to them in order to effectively utilize the "compromise" or "trade-off" negotiation process. (Competitive Achievers, Negative Loyalists). Combat by knowing enough about the other party to recognize which requirements are real requirements and which are red herrings.
J. Reluctancy. Playing the "reluctant buyer" or the "reluctant seller" may give increased leverage in the negotiation process. (Negative Loyalists). Once the other party knows you must do the deal, your negotiation leverage has decreased significantly or disappeared. Always maintain your "walkaway power".
K. Concession Counting. Successful negotiators often make a big deal of any concession made, even minor ones and red herrings, and get a counter-concession for doing so. (Meddling Helpers, Negative Loyalists).
L. Author of Documents. Always attempt to get control of the preparation of the legal documents, as they will almost assuredly be slanted, to some degree, to your position.
M. A Successful Negotiation. In a successful negotiation, both sides feel a sense of accomplishment, feel the other side cared, feel the other side was fair, would deal again with the other party and feel the other party will keep the bargain.
V. The Due Diligence Process
A. Seller's Provision of Information. As a buyer often has the ability to choose among alternative businesses to purchase, for a seller to achieve the highest sales price, most favorable terms and a quick closing, the seller must be prepared to provide pertinent information regarding the business in a highly organized and expedient fashion. In the case of financial information about the business, the seller should be aware that information reported to various taxing authorities, such as federal income tax returns, federal payroll tax returns and state sales tax returns generally will be more credible than internally generated financial statements and reports. Other third party information, such as bank statements, will also be considered highly credible as evidencing actual income and expenses. Therefore, inconsistencies among such data should be reviewed and handled prior to dissemination of information to the buyer. Additionally, audited or compiled financial statements by a reputable CPA firm should provide additional credibility, as well.
B. Early Initiation of Third Party Actions and Consents. Oftentimes, actions or consents of third parties may be required to properly accomplish the transfer of the business from the seller to the buyer. Early initiation of obtaining such third party actions or consents is imperative with respect to a timely closing. Third party action and/or consent is often involved where there are third party liens that need to be released, real estate leases to be assumed and customer/vendor/franchisor/licensor agreements to be assigned. Curing title to assets may be involved, as well, particularly for real estate, personalty subject to a security interest and intellectual property rights. Be sure to order early a title policy commitment for all real estate to be purchased and a UCC search on each selling party. All environmental studies, structural inspections and heavy equipment testing should be accomplished early, as well.
C. Quick Closing Desired by Seller. Particularly, the seller should desire as short a due diligence and document preparation period, as possible. As the time period before closing lingers on, there is more opportunity for a buyer to find a better deal. Furthermore, because knowledge of an impending sale generally spreads quickly to employees, suppliers and customers (often with detrimental effect), a long pre-closing period may have a chilling effect, not only with respect to the current buyer, but with future buyers, as well, in the event the current purchase falls through. Substantial earnest money, with specific time commitments for future actions, should be obtained by seller, particularly in view of the fact that a newly formed corporate shell will often be the party executing any binding agreement involving the acquisition as buyer.
VI. Certain U.S. Income Tax Considerations
A. From the Seller's Perspective. It is generally advantageous for the seller to obtain two U.S. income tax objectives when selling his business: (i) incur a single level of tax at (ii) individual capital gain rates.
One way to achieve these two objectives is for the seller to sell his equity interests in the entity conducting the business rather than the assets of the business themselves. However, in most scenarios, a buyer will not be willing to accept the risk of unknown or undisclosed liabilities that would carry over to the buyer in an equity interest purchase, in addition to buyer's unwillingness to purchase equity interests due to the different tax objectives of buyer discussed below. Therefore, a seller is often not able to successfully negotiate an equity interest sale.
Other than depreciation recapture (including amounts previously expensed under IRC §179) taxed at ordinary income rates, a seller can generally achieve these two objectives even when selling the business assets, rather than the equity interests, for businesses conducted by "pass-through" entities, such as partnerships, limited liabilities companies and S corporations. In such cases, the U.S. income tax objectives of both seller and buyer can generally be accomplished through an asset sale and purchase.
When selling a business conducted by a C corporation, with its inherent double U.S. income tax structure, consideration of the concept of "personal goodwill" discussed below may ameliorate the harsh U.S. income tax consequences to seller under the right circumstances.
B. From the Buyer's Perspective. It is generally advantageous for the buyer to purchase assets rather than equity interests in order to allocate the purchase price to depreciable or amortizable assets for subsequent U.S. income tax benefits.
This generally works out fine for both buyer and seller when the selling entity is a "pass-through" entity, such as partnerships, limited liability companies and S corporations, where the assets of the entity can be purchased without creating a double tax situation for the seller and, at the same time, allowing for allocation of the purchase price among depreciable or amortizable assets for future cost recovery deductions which will benefit the buyer.
When purchasing a business conducted through a C corporation, with its inherent double U.S. income tax structure, consideration of the concept of "personal goodwill" discussed below may ameliorate the harsh U.S. income tax consequences to seller and still allow future tax benefits to the buyer through future amortization deductions of goodwill intangibles.
C. Personal Goodwill. As many purchasers of corporate businesses are insistent on purchasing the assets of the business rather than the stock in the corporation, a double taxation situation occurs for the shareholders of a selling C corporation, a tax at the corporate level (without benefit of a lower capital gain tax rate) and another tax at the shareholder level.
A relatively new concept designed to, among other things, eliminate a substantial portion of the double taxation under the right circumstances is to recognize that a large portion of the "goodwill" value of a C corporation is not really goodwill of the corporation, but rather goodwill of the key employee/owner ("personal goodwill"). Accordingly, in the right situation, a large part of the purchase price could be allocated and paid directly to the key employee/owner and treated as the sale of a capital asset, resulting in one level of tax at individual capital gain tax rates. There are two key cases in this area: (i) Martin Ice Cream Company v. Commissioner of Internal Revenue, 110 T.C. 189 (1998) ("Martin Ice Cream") and (ii) William Norwalk, Transferee, et al v. Commissioner of Internal Revenue, T.C. Memo 1998-279 ("Norwalk").
In Martin Ice Cream, the Tax Court held that there is no saleable goodwill in a corporation where the business of the corporation depends on its key employees, unless the key employees had entered into a covenant not to compete with the corporation or another agreement whereby their personal relationships with clients become the property of the corporation. In Norwalk, the court held that the shareholder accountants in a liquidating accounting firm realized no taxable income for receipt of corporate goodwill, the goodwill already residing in the individual shareholder accountants absent any covenant not to compete or similar agreement with the accounting firm. But also see two recent contra cases: Larry E. Howard v. U.S., Doc 2010-17126 (E.D. Wash. 2010), personal goodwill not allowed where dentist was subject to a pre-existing covenant not to compete agreement with his wholly owned practice, and James P. Kennedy v. Commissioner, T.C. Memo 2010-206, personal goodwill payments treated as payments for services where seller worked for buyer for several years after sale of company.
Also to be considered is the principle that the presence of personal goodwill is presumably determined in a competitive context, not in a retirement context. That is, it appears that the issue is not whether the corporation could continue if the shareholder were to retire and not be active in the same line of business, but rather, it appears that the question is whether the corporation's business would follow the shareholder if the shareholder engaged in a competitive business.
The percentage of potential dollars of U.S. income tax saved from re-allocating each dollar away from corporate goodwill to personal goodwill is 29.7%, assuming a corporate tax rate of 34%, an individual capital gain tax rate of 20%, and non-application of the 3.8% Medicare surtax on the sale of personal goodwill (gain on sale of trade or business property exception), computed as follows:
|Scenario One: Sale of Assets, No Personal Goodwill
|Sales Proceeds
|Corporate Tax (34%)
|Remaining Funds Distributed to Shareholder
|Individual Dividend Tax (20%)
|Individual 3.8% Tax on Net Investment Income
|Remaining Funds for Shareholder After U.S. Income Taxes
|Scenario Two: Sale of Assets, With Personal Goodwill
|Sales Proceeds (Paid to Shareholder for Personal Goodwill)
|Individual Capital Gain Tax (20%)
|Remaining Funds for Shareholder After U.S. Income Taxes
|Difference: $0.80 - $0.503 = $0.297 or 29.7%
D. IRC §1060. IRC §1060 was enacted primarily to address certain problems encountered by the IRS with respect to the prevalent practice of inconsistent tax reporting by buyers and sellers of the tax consequences relating to their business sales and purchases. Sellers would tend to allocate the purchase price toward goodwill to obtain favorable capital gain rates and buyers would allocate the same amounts to depreciable tangible personal property to obtain depreciation deductions. IRC §1060 requires the buyer and the seller to allocate the purchase price amongst the purchased assets pursuant to the residual method of accounting. To help inform the IRS of such allocation, both buyer and seller are required to file IRS Form 8594 with their respective U.S. income tax returns in the year of sale in order to report such allocation. If the buyer and seller agree to a purchase price allocation in the acquisition documents, then the parties are required to report the U.S. income tax consequences of such sale consistent with such agreement.
VII. Definitive Agreements
A. Warranties and Representations. The seller naturally desires to receive the purchase price from the sale of the business with very limited rights of the buyer to obtain a refund back of all or a portion of the purchase price or to reduce or eliminate deferred payments. In addition to certain contingencies which may be placed on deferred payments, a buyer usually obtains warranties and representations from the seller, which if breached and causing damage to buyer, give the buyer certain rights against the seller. Attorneys for sellers typically attempt to restrict the warranties and representations to the basic ones regarding organization and existence, ownership of stock or assets, authority, no violation and no default. Buyer's counsel usually requires a myriad of additional warranties and representations, including accuracy of financial statements, absence of certain changes, tax matters, contracts and agreements, absence of liens, fringe benefits, pension and other retirement plans (ERISA matters), leases, insurance, intangible assets, permits, personnel data, labor relations, compliance with laws, inventory, transactions with related parties, environmental compliance, accounts receivable, customers and suppliers, improper payments, warranty claims, interests in customers and vendors, litigation and full disclosure. Particularly for larger transactions, the seller's attorney will be required to render a legal opinion as to the validity of certain warranties and representations. As a seller will often be a shell entity after the sale of the business and distribution of the sales proceeds to its owners, it is important from the buyer's perspective to have the ultimate recipients of the sales proceeds, usually the owners or shareholders, join in on the warranties and representations and assume joint and several liability with respect to breaches thereof.
B. Right of Offset. What may be of particular importance to a buyer in an asset acquisition is, not only the content of the warranties and representations regarding the purchased business, but the remedies available in the event of a material breach of any such warranties and representations. Successful implementation of a "right of offset" provision in the asset acquisition documents can completely (and more legally) switch the leverage regarding non-payment of future installments of the purchase price in favor of the buyer and away from the seller, as would be traditionally the case. A "right of offset" allows the buyer to contractually offset from future payments due the seller the amount of any damages suffered by the buyer in the event something is wrong with the acquired business in contravention of any warranty or representation made by the seller. This right is important for a buyer because hidden defects or difficulties involving a business may not be ascertained for a period of time after acquisition, notwithstanding any expansive due diligence work performed by the buyer prior to acquisition. The "right of offset" is not automatically provided for by operation of law and, if properly utilized, forces the seller to initiate court action to disprove the breach of warranty. In contrast, without a "right of offset", the buyer would be required under its contract to continue deferred payments of the acquisition price (and, thus, creating or expanding the seller's litigation war chest) and initiate an expensive and lengthy court action in a suit to recover damages. If properly drafted, the "right of offset" can apply to deferred payments made to the seller in the form of restrictive covenants, such as a covenant not to compete, and in the form of consulting or employee services if the seller (or its owners) continue to provide services to the acquired business.
C. Seller Considerations/Warranties and Representations. In the normal setting involving sophisticated parties, it is difficult for a seller to avoid extensive warranties and representations, often involving a "right of offset". However, important limitations on such warranties and representations often are not difficult to achieve. Since the extensive warranties and representations (and right of offset) usually result from the buyer's fears that its due diligence efforts cannot pick up every material defect, and that only a period of operation can make such defects discernible, the seller can often successfully obtain a removal or lapse of all or most warranties and representations after a reasonable period of time of buyer's operation of the purchased business (for example, one to two years from closing). Additionally, a limitation on the amount of damages that can be recoverable against the seller can be limited to a specified dollar amount ("ceiling"), oftentimes the amount of consideration to be received by seller in connection with the sale of the business or a lesser amount. Furthermore, a "basket" amount can be specified that any damages must exceed before the buyer is entitled to recover any of the purchase price from the seller (for example, an amount equal to 1% of the purchase price).
D. Other Closing Documents. Aside from the definitive basic agreement, usually in the form of an asset purchase agreement, a stock purchase agreement or a merger or conversion agreement, there are other numerous important legal documents associated with the business acquisition. There will be various documents relating to title of the purchased assets and the release or assumption of prior liens, such as bills of sale, warranty deeds, releases of liens and UCC-3 termination statements. In the case of a seller financed or leveraged buyout transaction, there will be various documents evidencing seller's right to deferred payments, such as promissory notes, security agreements, deeds of trust, UCC-1 financing statements and/or guarantee agreements. In connection with leased assets, there may be lease agreements, estoppel certificates from existing landlords and assignments of leases, including landlord consents. For intellectual property rights, there may be patent assignments and license agreements to be obtained. Oftentimes, there are restrictive covenant agreements, providing for covenants not to compete and nonsolicitation prohibitions, as well as employment agreements and/or consulting agreements, whereby the seller, or individuals affiliated with the seller, continue to work for, and receive payments from, the buyer in the future.
VII. Continuing Relationship. Due to the continuing existence of seller financing in many business acquisitions and the often continuing relationship between seller and buyer through employment and consulting agreements, it is important to recognize that often the relationship between buyer and seller does not end at closing, but rather, in a real sense, only begins. The structuring and documentation of all of the important aspects of this ongoing relationship is of vital importance. Throughout the negotiation process and the document preparation stage, the parties must always be cognizant and deal effectively with the ramifications that there will be, in most likelihood, a continuing relationship between the parties, oftentimes for an extended period of time after the transfer of the business from seller to buyer.


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Dude Gets Metro Map Tattooed On His Arm [Washington City Paper] I thought the metro map was the lamest tattoo ever, until I googled "lamest tattoo ever" and spent the last twenty minutes looking through the results. Metro map is still pretty lame though.
Vandals Topple Ten Commandments Monument [Huffington Post] My first reaction upon reading about this was to think, "I bet I'm Facebook friends with the people who did it!" (After an inspection of my friends list, I've gotten it narrowed down to two, three names.)
Ledroit Park Market For Sale! [Urban Turf DC] Would you like to own an upscale corner store (the liquor license would transfer with the sale!) in one of the city's hottest neighborhoods, and live above it in a massive two-units-merged-into-one loft space? Of course you would! Too bad that it already got an offer and is as good as sold! Ha ha! (God, I'm horrible.)
Kegger House Rental Listing Irritates Clarendon Neighbors [ARLnow] The ad for this house describes it as "stumbling distance" from the Clarendon strip, but I must be reading it wrong, because it sounds like it's saying you have to PAY a thousand a month to live there, but in all seriousness, they must mean that they'll pay YOU a thousand a month to live there. Because no one would pay money to live off the Clarendon strip, right? RIGHT?!
Contractor Needed to Finish National Mall Levee [DCist] No big deal, the nation's capital is just COMPLETELY VULNERABLE TO CATASTROPHIC FLOODING UNTIL IT'S FINISHED. I think this is going to be my new excuse when people chide me for drinking before 5PM. "We could be hit with a terrorist-induced flood attack any second, I'm living every day like it's my last!!"

subset: commoncrawl


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Target Compiler Technologies is the leading provider of retargetable software tools for the design, programming, and verification of application-specific processors (ASIPs). ASIPs are key building blocks of both single-core and multi-core systems-on-chip (SoCs) that power today's electronic systems.
There are no discussions here currently, but as they appear they might have answers you need.


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- Conference date: 30 Jul-3 Aug 2001
- Location: Berkeley. California (USA)
The leptodermous approximation is applied to nuclear systems for The introduction of surface corrections leads to anomalous caloric curves and to negative heat capacities in the liquid-gas coexistence region. Clusterization in the vapor is described by associating surface energy to clusters according to Fisher's formula. The three-dimensional Ising model, a leptodermous system par excellence, does obey rigorously Fisher's scaling up to the critical point. Multifragmentation data from several experiments including the ISiS and EOS Collaborations, as well as compound nucleus fragment emission at much lower energy follow the same scaling, thus providing the strongest evidence yet of liquid-vapor coexistence.
Key Topics
- Liquid surfaces
- 2.0
- Surface phase transitions
- 2.0
- Compound nucleus
- 1.0
- Critical point phenomena
- 1.0
- Equations of state
- 1.0
Probing Inflation with CMB PolarizationDaniel Baumann, Mark G. Jackson, Peter Adshead, Alexandre Amblard, Amjad Ashoorioon, Nicola Bartolo, Rachel Bean, Maria Beltrán, Francesco de Bernardis, Simeon Bird, Xingang Chen, Daniel J. H. Chung, Loris Colombo, Asantha Cooray, Paolo Creminelli, Scott Dodelson, Joanna Dunkley, Cora Dvorkin, Richard Easther, Fabio Finelli, Raphael Flauger, Mark P. Hertzberg, Katherine Jones‐Smith, Shamit Kachru, Kenji Kadota, Justin Khoury, William H. Kinney, Eiichiro Komatsu, Lawrence M. Krauss, Julien Lesgourgues, Andrew Liddle, Michele Liguori, Eugene Lim, Andrei Linde, Sabino Matarrese, Harsh Mathur, Liam McAllister, Alessandro Melchiorri, Alberto Nicolis, Luca Pagano, Hiranya V. Peiris, Marco Peloso, Levon Pogosian, Elena Pierpaoli, Antonio Riotto, Uroš Seljak, Leonardo Senatore, Sarah Shandera, Eva Silverstein, Tristan Smith, Pascal Vaudrevange, Licia Verde, Ben Wandelt, David Wands, Scott Watson, Mark Wyman, Amit Yadav, Wessel Valkenburg and Matias Zaldarriaga
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from Wiktionary, Creative Commons Attribution/Share-Alike License
- n. a set of rules to guide behaviour and decisions in a specified situation
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
- n. a set of conventional principles and expectations that are considered binding on any person who is a member of a particular group
See code and conduct (Wiktionary)
Sorry, no example sentences found.


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Stealth Playground Tour
January 12, 2013
Today Mouse and I are continuing our tour of Alexandria-area playgrounds with a stealth stop at Skyline Plaza. Mouse saw the oddly suspended play structure as I was executing a U-turn on King Street where it becomes Leesburg Pike and clamored to see it. It's a nice day out, so I didn't mind an excuse to avoid going home.
Verdict: not crowded. Interesting if your kid isn't afraid of heights. Even daredevil Mouse, who generally is not scared of heights, felt like everything was just a little too high off the ground. Also, I kept wondering when someone was going to come tow my car or kick us out.
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Geezeo said it has signed the $341 million Call Federal Credit Union in Richmond, Va., to the Tolland, Conn., company's personal financial management and integrated marketing platform.
OCEAN CITY, Md.— One of the many lessons Kelley Parks learned in going through the process of rebranding Call Federal Credit Union was that loyalty to your founders is important in rebranding your organization.
Rebranding calls for attention to foundations of organization getting the makeover, marketing expert tells MDCCUA.
Richmond, Va., CU becomes 16th to commit to Connecticut firm's online budgeting and marketing solution.


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Pink Panthers
Total Time
Prep 2 mins
Cook 1 hr
I had one of these at an Embassy Suites hotel once. Very, very good!
Ingredients Nutrition
- 2 cups carbonated water
- 1⁄2 cup grenadine
- 6 tablespoons heavy cream
- Combine the soda water and grenadine. Chill for about an hour. Pour into two glasses. Top each with three tablespoons cream.
Most Helpful
Made with grandbabe. Gee, that smacks of work, doesn't it? Made for Think Pink Recipe Tag.
I absolutely love homemade sodas and this treasure does not disappoint. I can't wait to share this with my granddaughter she is going to love it. What's not to like it tastes great and it is bright pink. The recipe was quick and easy to follow with devastating effects, it was so good that I immediately had to have another. Thank you for sharing this lovely recipe that I will be making often. Made for Think Pink 2013
Tasty drink that is so pretty and pink in the glass. Couldn't be easier to make. Thanks Baking*Belle Bullwinkle.


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Definition of parenthesis
parenthesesplay \-ˌsēz\
1 a : an amplifying or explanatory word, phrase, or sentence inserted in a passage from which it is usually set off by punctuation b : a remark or passage that departs from the theme of a discourse : digression
3 : one or both of the curved marks ( ) used in writing and printing to enclose a parenthetical expression or to group a symbolic unit in a logical or mathematical expression
parentheticallyplay \-ti-k(ə-)lē\ adverb
Origin and Etymology of parenthesis
Late Latin, from Greek, literally, act of inserting, from parentithenai to insert, from para- + en- en- + tithenai to place — more at do
First Known Use: circa 1550
Other Grammar and Linguistics Terms
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This print started out as a baseball card more than twenty years ago. Every aspect of it is designed to preserve the original look and feel of the card, from the printing pattern to the slightly worn edges. In fact, this print started by finding the actual card in our vault and then painstakingly re-mastering it with a team of designers. The authenticity extends to manufacturing; each print is made on high-quality, cotton fine art paper that measures 1/64 inches in thickness. Framed prints feature 2-inch flat wood or metallic frames with high-end, glare-resistant glass. And all prints are officially licensed by MLB and the National Baseball Hall of Fame.
Bill Freehan and his former Tigers teammate, Mickey Lolich, will always be intertwined. Freehan was the starting catcher for 325 of Lolich's starts, a record for any pair. Freehan retired after the 1976 season, finishing with a .262 average, 200 home runs, 11 All-Star nods and five Gold Gloves.
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I'm chuckling a bit at my last post. I'm not usually one to overburden myself, and I generally settle into a nice rhythm of craftiness, laziness, and quality family time during the holidays. Not this year! I decided it'd be fun to have this be the year of handmade Christmas gifts, which did turn out to be fun and more special (on my end, at least). I think I may do it again, but for heaven's sake, someone please remind me to START EARLIER!!
Oh, and there were just a few other errands and projects thrown in for good measure. Just to give you an idea, in the last few weeks, I…
- Prepped for two birthday parties
- Made a birthday cake (hers is prettier) and a few goodies for neighbor gifts
- Made several errand runs, each with the world's most ridiculous and belligerent almost-three-year-olds in tow (can you blame me for doing most of my Christmas shopping online?!)
- Took the van in to be repaired before its warranty expired
- Sang at a Christmas dinner party, and made giant pageant animals for another
- Helped my brother purchase a Christmas gift from a cruise ship
- Attended extra evening choir practices for the world's most ambitious church choir undertaking
- Took myself or kids to four different doctors' appointments (Ear infections! Blood tests! Barfing!)
- Made dinner for a sick friend from church
- Hand-made presents for my brother,
his two sweet-pea daughters
and his son (there were velcro-covered wiffle balls to go with this🙂 ),
both of my parents (patterns here, for knitters!),
the in-laws (I forgot to take a picture!), some ladies from church (recipes here!),
a family friend (pattern!),
and my grandmother (pattern).
And all this, on top of all my usual duties as mom, chef, maid, Cub Scout leader, and wife. All I can say is, I need a nap. Please don't wake me until 2013.🙂


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Rizzo, Leonardo MD*; Marini, Maurizio MD*; Rosati, Chiara MD*; Calamai, Italo MD*; Nesi, Michela MD*; Salvini, Roberto MPH†; Mazzini, Cinzia MD‡; Campana, Fiamma MD‡; Brizzi, Enzo MD§
*Department of Critical Care Medicine and Surgery, Section of Anesthesiology, †Department of Epidemiology, ‡Department of Oto-Neuro-Ophthalmological Surgery, Section of Ophthalmology, §Department of Pathologic Anatomy, University of Florence, Florence, Italy
Accepted for publication July 16, 2004.
Address correspondence and reprint requests to Leonardo Rizzo, MD, Department of Critical Care Medicine and Surgery, Section of Anesthesiology, University of Florence, Viale Morgagni 85, 50134, Florence, Italy. Address email to email@example.com.
We evaluated the efficacy and safety of a single injection technique with a small volume of anesthetic for ocular peribulbar anesthesia. We included 857 patients undergoing various ophthalmic procedures. Anesthesia consisted of a medial percutaneous injection of 5–6.5 mL of 2% lidocaine. At 2 min 85.6% of the patients had a motor block of at least 50% and at 5 min 78.6% had a motor block >80%. After 5 min 100% of the patients had adequate surgical anesthesia. There were no serious block-related complications. The described technique is a simple and satisfactory alternative to the classical techniques
Ophthalmic procedures such as cataract extraction with phacoemulsification can be performed with either topical or regional anesthesia (1). Regional anesthesia is still widely used in cases of difficult surgery and extended time surgery (1).
Retrobulbar anesthesia is the standard technique for regional anesthesia in ophthalmic surgery, but complications of this technique, although relatively uncommon, can be catastrophic. However, the complications associated with retrobulbar anesthesia have been subsequently described with peribulbar anesthesia with less, but still unacceptable, frequency (2–7).
An overview of the ASA Closed Claims Project database reported that the most common disabling injuries associated with regional anesthesia are related to nerve blocks of the eye (8). These potential risks led to the proposal of a single, rather than multiple, injection technique of peribulbar and episcleral anesthesia in order to decrease the risks of complications (9–12).
The purpose of this study was to evaluate the efficacy and safety of a percutaneous peribulbar single injection technique of regional anesthesia with a small volume of anesthetic for various ophthalmic procedures.
The study was conducted after approval of our institution's local ethics committee and patients' verbal, informed consent. Eight-hundred-fifty-seven consecutive patients scheduled for elective ophthalmic procedures at Department of Oto-Neuro-Ophthalmological Surgery, Section of Ophthalmology, University of Florence from September 2001 to March 2003 were included. Exclusion criteria were contraindications to ocular regional anesthesia and patient refusal. The patients were not fasted. A few uncooperative patients (approximately 8%) were premedicated with midazolam IV (0.02 mg/kg) 5 min before the block. All patients had a peripheral IV line inserted and the usual standard monitoring was used.
The injections were given with a 25-gauge, 16-mm bevel disposable needle. The anesthetic was 2% lidocaine; volume ranged from 5 to 6.5 mL on the basis of dimension of the eye socket. The patients were asked to move their eye so as to expose the area to be injected (to 10 o'clock for right eye and to 2 o'clock for left eye).
The injection site was percutaneous and limited superiorly from inferior lacrimal canaliculus, median from lateral margin of nose, laterally from imaginary perpendicular line that join inferior lacrimal papilla to inferior margin of orbit and inferiorly from inferior margin of orbit (Fig. 1).
The needle was advanced percutaneously in an antero-posterior direction for half of its length (never more than 10 mm) (Fig. 2a) and later obliquely in the direction of the optical foramen until the needle was on the same plane of the bony margin of orbit (Fig. 2b). After aspiration, the anesthetic was injected in approximately 30 s.
An initial transient fullness in the supero-internal region of superior lid was predictive of successful blockade. After the needle was removed, moderate digital massage of the eyeball and compression of the site of injection were performed. Patients were observed carefully during the injection and immediate complications were noted.
Akinesia of the globe and eyelids was assessed at 2 min (T1) and 5 min (T2). A 12-point scale (13) was used (each of the 4 rectus muscles and each lid was scored from 0 to 2; 0 = no block, 1 = partial akinesia, 2 = total akinesia).
Five-hundred-forty-two female (mean age 72 ± 11 yr) and 315 male (mean age 70 ± 12 yr) patients (ASA physical status I–III) were studied. The procedures were 517 phacoemulsifications and posterior chamber artificial lens implantations, 137 open globe procedures for lens extraction (intracapsular or manual extracapsular extraction), 109 trabeculectomies, and 94 other procedures including vitrectomy and retinal surgery.
At T1 85.6% of patients had a motor block of at least 50% (score 6 of 12) and at T2 78.6% of patients had a motor block >80% (score 8 of 12). After 7 min 100% of patients had adequate anesthesia to proceed with and complete the surgery. Only 107 patients required midazolam 0.015 mg/kg intraoperatively.
Complications included one case of inferior lid hematoma for perforation of a superficial vein tributary of the angular vein and four cases of chemosis that did not hinder surgery. There were no cases of perforation of the globe, retinal or optic nerve damage or orbital hematoma or postoperative diplopia.
In this large series of patients peribulbar anesthesia by a medial percutaneous single injection was a valid alternative technique for ocular regional anesthesia because of the infrequent complications we observed. This site of injection is relatively avascular, which may decrease the risk of hematoma. Indeed, we noted no orbital hematoma in this series. Because the insertion of the needle is limited to the anterior orbit, ophthalmic artery, optic nerve or retinal injury is unlikely. It should be stressed that akinesia and analgesia of the globe and eyelid were obtained with our technique using a very small volume of anesthetic (no more than 6.5 mL).
To determine the exact pattern of distribution of anesthetic fluid in this type of regional anesthesia in 27 patients we performed B-scan ultrasonography before (Fig. 3, left) and at few minutes (Figs. 3, right, and 4) after the administration of anesthetic (14). After the injection, the fluid tracked behind the globe in the sub-Tenon capsule space (Fig. 4, left). Posterior, the fluid around the optic nerve developed a characteristic T sign (Fig. 4, right). The fascial sheath of the eyeball (Tenon's capsule) is a fibrous layer that surrounds the eyeball from the optic nerve to the corneal ring. It is a thick membrane at the equator of the globe, where it is pierced by the rectus muscle tendons and is continued by the muscle sheaths. The episcleral space is a virtual gliding space between the sclera and the fascial sheath of the eyeball. The sensitivity of the eyeball is provided by the ciliary nerves, which cross the episcleral space after they emerge from the globe. We confirmed that a small volume of local anesthetic (5–6.5 mL) injected in this space is guided to surround the eyeball and produce analgesia. The fascial sheath of the eyeball extends to the rectus muscle sheaths. This explains why the anesthetic is preferentially guided to those muscle sheaths to produce good akinesia. Furthermore the fascial sheath of the eyeball guides the injected solution to the lids, especially to the orbicularis muscle. This explains how we can prevent blinking during surgery without performing any facial nerve block.
Our medial single injection technique is a simple and satisfactory alternative approach for ocular regional anesthesia. The advantages include decreased pain with percutaneous and short needle insertion, decreased volume of anesthetic, single rather than multiple punctures, puncture in a relatively avascular area, and a needle path that is less subject to misdirection.
© 2005 International Anesthesia Research Society
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|By Scorpsjl (Scorpsjl) on Sunday, May 02, 2004 - 02:00 pm: Edit
Who here thinks they're gonna take math 55 next year? personally, i'm pretty sure i'll opt for it over 25, tho i also want to take physics 16, and i dunno if i'll be able to deal with the work from both (can anyone say how much work 55 REALLY gives? I know it depends on the prof-does anyone know who's gonna teach it next year?)
|By Vecter (Vecter) on Sunday, May 02, 2004 - 05:41 pm: Edit
i'm guessing ur a MOPer?
|By Nifty101 (Nifty101) on Monday, May 03, 2004 - 09:22 pm: Edit
what is math 55, anyone like to explain please?
|By Vecter (Vecter) on Monday, May 03, 2004 - 10:17 pm: Edit
math 55 is the hardest freshman undergraduate math class in the country. basically kids on the national math team (a.k.a. MOP-Math Olympiad Program) and the International Math Olympiad team (IMO) take it
for math geniuses :/
|By Eurostar (Eurostar) on Tuesday, May 04, 2004 - 05:11 am: Edit
I am taking 21 or possibly 23
There is no way I would take 55. Don't torture yourself right away..
Everyone take Physics 16, though!
|By El_Diablo (El_Diablo) on Tuesday, May 04, 2004 - 01:02 pm: Edit
how do u know the courses?
|By Monekit (Monekit) on Tuesday, May 04, 2004 - 06:24 pm: Edit
|By Kenenisa (Kenenisa) on Tuesday, May 04, 2004 - 08:06 pm: Edit
At the risk of sounding like a jerk (sorry in advance):
Yeah, I'm sure a school like Caltech doesn't offer anything even close to as challenging as Math 55, which according to the site is basically an accelerated math class covering the first couple of years of college math.
I know someone indirectly who is finished with undergraduate math, and he is still in high school.
|By Scorpsjl (Scorpsjl) on Wednesday, May 05, 2004 - 09:15 pm: Edit
Kenenisa, i'm assuming that was sarcasitc. Indeed Math 55 has been heralded by many sources as the hardest undergrad math class in the country. This isn't to say that Caltech doesn't have a very hard honors class, or maybe even (hypothetically) a harder one, but Math 55's reputation is pretty respected. It covers Single and multivariable calculus, differential equations, linear algebra, and some topology (basically, the first 3 years of college math for a 'normal' math major, though i say that in quotes because many math majors, not only at harvard, are accelerated). The only topics left in normal undergrad math are analysis, and possibly some algebra. And to address the second point about your friend, many (most?) 55'ers have already seen all or most of the topics covered by the class. What's different about 55 is the level of depth and abstractness at which the topics are covered. The class is very intensive and proof based, as well as fast moving. what proof based means is that unlike in hs math, where you have to apply a theorem or algorithm that was already proved in class to examples, you will have to first prove that theorem or algorithm yourself, given the background from class. math 25 and i think 23 are proof-based also, but nowhere near as intense as 55. anyway , i think i'm gonna take it-will be insane, but an awesome experience. anyone else with me?
|By Uncchlocalmayor (Uncchlocalmayor) on Thursday, May 06, 2004 - 04:32 am: Edit
Kenensia, are you talking about Anders Kaseorg who finished out the undergrad. math classes at uncc by his junior year in hs? yeah, i was in the same mathcounts group w/ the kid back when i homeschooled. anywho, later.
-UNC c/o 2006, hava'd sucks
|By Corny (Corny) on Thursday, May 06, 2004 - 01:02 pm: Edit
Math 55 is definitely not for everyone. Even if you received a 5 on your AP Calc test, don't take Math 55 unless you already know how to write proofs very well or you'll regret it.
Most of the people in that class have been doing proofs for years and you'll never have time to catch up. Math 25 would be a safer bet but that class is no piece of cake either. At least in Math 25 you'll have fellow students who have never done real math proofs before and will suffer along with you.
|By Kenenisa (Kenenisa) on Thursday, May 06, 2004 - 05:36 pm: Edit
It definitely was not sarcastic. To say that any class is the hardest undergraduate math class is absurd. What is an "undergraduate math class?" The person earlier said that it's the "hardest freshman math class" - what the heck is a freshman math class? Some people start with college algebra or calculus, for some people all of the topics you said would be review as a freshman, which you acknowledged. So basically, if your freshman year is the hardest, you're saying a year of review is the hardest year you have in college as a math major? I just find that hard to believe. I have a friend who is a junior in HS and he will be done with everything you said is in Math 55 by the time he is out of HS, and he just isn't that smart. If that's seriously as hard as math gets, then math is an easy major, and I really doubt that's the case. I have huge respect for math. I'm no math whiz compared to these math team guys (although I did make an 800 on IIC and I did just rock the BC calc exam), so maybe I'm barking up the wrong tree, but when I see someone coming onto a forum saying "my freshman math class at Harvard is the hardest math class in the nation," I feel like he is probably full of it, especially considering some people are DONE with undergrad math before they even finish HS... it's a moot point anyway.
Anyway, I am definitely jealous of you guys who will be in a class like that. I wish I had used more opportunities to take college math in HS. Best of luck to you in that class, I'm sure it is definitely difficult
Oh, and I understand the difference in applying rules and writing your own proofs, but like I've said a hundred times, I just don't see how a year of what for many people is review could possibly be the hardest undergrad math course in the nation when there's crap like chaos math (I don't even know what that is, I just heard the name from Good Will Hunting!).
|By Vecter (Vecter) on Thursday, May 06, 2004 - 05:49 pm: Edit
i know someone taking 55 next year, he did a research project on de Sitter space. in case you don't know what de Sitter space is (and I still don't haha), here's a definition I found online:
I think it's funny how almost EVERY WORD in that definition requires a definition in itself
that's 55 for ya :-P
(btw i'm just a high school BC-er who bows down to MOP/IMOers)
i also saw a copy of his paper, more equations than words lol
tho it's interesting b/c he never did MOP or IMO, i guess he's just a closet genius who doesn't do those sorts of competition, but I can definitely see him doing decently in 55, if not well
|By Fprescott54 (Fprescott54) on Thursday, May 06, 2004 - 07:27 pm: Edit
Vecter I agree I also bow down to IMO/ MOPpers
Kenenisa, you obviously have not heard about 55. I have a friend who is a former MOPper and struggling in 55. I don't think it is hard b/c of its set curriculum, its considered to be incredibly hard b/c they gather the BEST freshman mathematications in the country and put them in a proof-based class determined to study as much obscure math as possible. It is a class only offered to freshmen and is known for 30-page problem sets. I don't think "upperlevel" math classes like abstract algebra are necesarily "harder", but math 55 is definately "harder" b/c you are not just learning about new topics like for example taking Calc 2 after taking Calc 1, you are probing the entire reasoning behind Calc 1 and trying to really understand what math is about.
|By Kenenisa (Kenenisa) on Thursday, May 06, 2004 - 08:11 pm: Edit
Ok, so be it. If a freshman course that basically covers from calc through linear algebra is the most difficult math course in America, then the future of math is disheartening. However, I will shut up because I freely admit I do not know what I'm talking about, it just surprises me greatly (and I still think it's probably very wrong, but like I said I have no facts to back it up so I won't keep arguing).
|By Corny (Corny) on Thursday, May 06, 2004 - 08:29 pm: Edit
The best analogy is learning a language.
If somebody told you that they were going to cram four years of language learning into a single year, would you think that was difficult? Yes, of course, because you'll be learning the material at such a fast rate.
And then if they told you that you would have to study that language with gifted language learners, would that make the class even harder? Yes, because the faster people learn, the faster the teacher can teach the class. That means there is no time for review because you have to move on to the next topic.
Math 55 is that type of experience.
|By Scorpsjl (Scorpsjl) on Friday, May 07, 2004 - 12:39 am: Edit
corny-pretty good analogy
kenenisa- first of all, if you reread your first post, you 'were' being sarcastic-"yeah, i'm sure that caltech doesn't etc.. etc"...that was just how you were making your point ( you even prefaced it with "i dont wann be a jerk, etc" and i was just making sure thats what you meant.
secondly, what you don't seem to understand is that math 55 doesn't cover the HARDEST topics in mathematics, it's just that it's the hardest class. And by that we mean the most intensive, and most time-consuming, not necessarilly the most intelligence-demanding. For example, (although linear algebra and calculus can be very difficult and deep if one considers them in enough detail), there are many fields of mathematics that are more complicated than those covered in 55 that, in a normal math progression, come in the upperclass years of undergrad and in grad school. However, these classes are taught much more slowly than 55, and the students have more time to go over what they have learned, do problems, and really understand what is going on. Yes, these topics are "harder", as you say, and presumably there are some people who just won't get them, ever, although these same people might be able to get calc and linear algebra if they try hard enough. But these same people would crackle and burn in 55. do you see the point? and all of your arguments about "really smart undergrads who take all sorts of math in hs" don't really make sense, because, though i won't get into an argument of overall quality of school or even department, it is hard to argue with the statement that harvard gets practically all the best pure math students in the country (even over MIT, which really has a much better engineering program than pure math, tho must people aren't aware of this). And all of these best math students, the steven byrnes and the gabriel carrols, etc. etc, the smartest math majors in the country, take 55 (instead of skipping it and going into grad classes as freshman). and are challenged by it, and have a lot of fun in it. Our assertions are definitely correct, and i still don't understand why you find it so hard to believe, tho as you 'freely admit', you have no idea what you're talking about (i.e. the 'inside' math game), and so i'll excuse you.
vecter- with respect to your friend, he doesn't necesarilly have to be a "closet" geniuses. there are many mathematicians who are very good researchers, great at grasping concepts and coming up with new ideas, but these same people are not great at math competitions, which utilize different skills than research (fast thinking, quick problem solving, resourcefulness). although many people are good at both, many awesome mathematicians are good at research but not at competitions (the opposite isn't really true -- it's hard to say that many awesome mathematicians are good at competitions but not at research, because, ultimately, it is research that is important).
aaah can't wait for 55. it's why i chose harvard over stanford. both have great depts (even heard stanford's was friendlier) - but like all of you are saying, it's the students (all the MOP'ers, intel finalists, semifinalists and isef winners in math, etc...) who go to harvard that make it the best.
|By Vecter (Vecter) on Friday, May 07, 2004 - 10:08 am: Edit
lol yeah i think there are at least 11 intel finalists going to harvard this year, but among them only two are doing math, the kid I mentioned before and another one from NY.
mit has 8 grr, but we got boris ;)
|By Ambitiousyokel (Ambitiousyokel) on Friday, May 07, 2004 - 10:24 am: Edit
Awesome. That kid whipped my ass in a chess tournament in sixth or seventh grade. B*tch-slapped me, as it were.
|By Corny (Corny) on Friday, May 07, 2004 - 02:36 pm: Edit
I'm not sure if the process has changed but a few years ago, Math 25 and Math 55 met together for the first few weeks and then only those who did extremely well on the homework assignments were asked to join Math 55. The rest remained in Math 25. I guess it was a way to weed out those who weren't good yet at writing proofs and solving abstract problems.
Does anyone know if that is still the case or can a student go directly into Math 55 now?
|By Vecter (Vecter) on Friday, May 07, 2004 - 02:56 pm: Edit
hehe ambitiousyokel are you talking about amos lubin? i didn't know he played chess. how do you know him?
|By Kenenisa (Kenenisa) on Friday, May 07, 2004 - 06:00 pm: Edit
You're right about the sarcasm - I misunderstood what you were saying. I had forgotten exactly what I posted, and I thought I had just said "there's no way Math 55 is that hard" and then you asked "are you being sarcastic." Sorry about that.
And anyway yes I can understand that perhaps it has the most "work" of any class, I was just very taken aback by "hardest." In a way I was partially correct in that, in my opinion, most people when they think about "hard" math classes think of stuff that is difficult to comprehend. At least I do, and that was my entire point, but basically I will concede that perhaps it has the most work of any traditional undergrad math course (although, of course, the real super geniuses as seniors probably are doing independent studies where they are creating new theorems working 8 hours a day, but anyway I'll just leave it at that )
Good luck in math 55.
|By Almostdead (Almostdead) on Saturday, May 08, 2004 - 04:19 pm: Edit
math 25 and 55 are taught separately to give the students the opportunity to shop both.
math 55 is NOT simply cramming 3 or 4 math classes into one. While the book says it's on differential equations, mv calc, etc... it's NOT. DEFINITELY NOT. It goes waaaaaaaaaay beyond normal calculus into algebra, Lie algebra, real/complex analysis, Fourier analysis, and... well I don't exactly know what they've done, but even IMO winners have trouble in that class. A lot of trouble. I've heard only one other math class offered for undergrads at Harvard can match 55's difficulty. Even the other classes in the 100s or 200s aren't as hard. Or so they say. professor in that class will expect you to have already learned everything, so he can just go straight to the really really really theoretical stuff.
Hmm what else... oh yeah... 25 (which I am taking). Also do NOT take this class if you haven't done any proofs before. Well, I don't know who's teaching it next year.... but this year we had a really demanding professor... and well, 16 students dropped after the first semester, making 25 an even smaller class (10 studnets) than 55 (18 students).
|By Scorpsjl (Scorpsjl) on Saturday, May 08, 2004 - 10:10 pm: Edit
Almostdead- are you taking 25 this year? Is there only one section? If so, I must have seen you... I sat in on the monday 25 class during prefrosh weekend. Are you in the class with all of the stuy people (alex ellis, joel lewis, alex levin), and the french guy? It seemed like a good class, but i still want to try for 55. i know a few people who are in it, and although i don't know how they're doing, they aren't godly at math. tho joel lewis is, and he's not taking it, which depresses me a little... how much work a week do you get from 25?
Are you a math major? If so, i'll probably run into you next year...
|By Scorpsjl (Scorpsjl) on Saturday, May 08, 2004 - 10:12 pm: Edit
vecter-is amos the tall, quiet, sort of oddball guy?
I might have gone to HCSSiM with him
|By Vecter (Vecter) on Saturday, May 08, 2004 - 10:21 pm: Edit
yeah Scorpsjl, very shy guy lol, took me a week to be able to get him to talk in a normal conversation
what's HCSSiM?
|By Almostdead (Almostdead) on Saturday, May 08, 2004 - 11:14 pm: Edit
scorpsjl: lol yeah, exactly that class. are you from stuy? good luck on shopping 55 next year... heh... i was there for two days and then i realized it was impossible for me to follow. (i hadn't had any math beyond calc BC....)
i'm definitely NOT a math major... prolly physics... math 25 showed me that i am horrible at math in a most efficient way. =(
|By Scorpsjl (Scorpsjl) on Saturday, May 08, 2004 - 11:20 pm: Edit
HCSSiM is the hampshire college summer studies in mathematics, a math summer program at hampshire college in amherst, mass. It's not super well known and super rich like RSI (nor is it focused on research like RSI)-it's more like PROMYS for (in my opinion) smarter people. (Though i really have no idea what they do at promys so i dunno). The director is a new-age mathematician named David Kelly, and he and all the other teachers there are incredibly smart. google it to get their website (hcssim.org)
vecter-are you going to ISEF?
|By Scorpsjl (Scorpsjl) on Saturday, May 08, 2004 - 11:28 pm: Edit
almostdead- yeah from stuy...
physics major? so you're like alex ellis, physics and math? he told me the physics majors, and espeically the math/physics people, were all pretty tight-knit. sounds cool. With no math beyond calc, it's probably pretty impressive that you're still in 25 right? I guess i just don't like people quitting on math, (usually it's because they think they're bad when they're really not) because it's so much fun! But it does get so esoteric sometimes, i might end up doing somethign applied too. i was thinking biology maybe instead of physics tho. how's your physics class?
|By Vecter (Vecter) on Sunday, May 09, 2004 - 12:46 am: Edit
naw i got shafted by regionals, gl there (i guess you did a math proj?). i saw a commercial for isef, looked really cool esp. @ the end @ the awards ceremony
i dunno how much freedom they give you there, but milk every ounce of it lol
|By Jab93 (Jab93) on Sunday, May 09, 2004 - 03:40 am: Edit
I graduated Harvard in 1993 with a degree in Physics and Astrophysics... then, there was only 3 options for the multivariable calculus/linear algebra track: 21 (regular), 22 (physics oriented), 25 (theoretical math oriented)...
For those who are physics/chemistry/engineering oriented, Math 21 is probably the best choice...
it is a very practical, problem-solving oriented track that is incredibly useleful in solving actual physics problems that you will encounter in your science courses...
The vast, vast majority of physics, astro, chem, geo, bio, etc concentrators take math 21.
Math 22 is more theoretical physics oriented... the funny thing is... my friends who took it didn't learn any practical techniques in solving actual problems... you learn math that you won't need until you get to graduate level physics, but in the meantime, you learn nothing of practical value for the physics courses you take as an undergrad.... my physics major friends who took this course regretted it...
Math 25 (and I guess now 55) is truly only for hardcore theoretical math types and physics people who want to focus on theoretical mathematical physics.... you won't learn anything of use whatsoever in solving real-world math problems that you will encounter in science or engineering...
By the way... most physics majors follow math 21 with the Applied Math 105ab sequence (complex variable analysis, partial differential equations, and fourier analysis)... which is by far the absolute most useful math sequence I have ever taken... I went on to get a PhD in astrophysics and I am now a astrophysicist... and I use the applied math I learned in those two courses every single day of my career.
|By Cosmology2020 (Cosmology2020) on Saturday, May 22, 2004 - 12:39 pm: Edit
do any other colleges offer a class similar to math 55 or math 25?
|By Corny (Corny) on Sunday, May 23, 2004 - 01:24 am: Edit
A lot of top schools (princeton, columbia,etc) offer honors math courses like math 25 but not math 55. At least, I don't know of a school that does.
|By Irock1ce (Irock1ce) on Sunday, May 23, 2004 - 04:14 pm: Edit
Berkeley's 53/54H maybe? Probably not.. but it definitely isnt TOO far behind in difficulty.. especially when you get a professor who speaks broken english.
|By Vecter (Vecter) on Monday, May 24, 2004 - 02:55 pm: Edit
lol Irock1ce, I doubt Math 55 is difficult b/c the professor is a poor communicator ;)
if that were the case then I took a VERY hard multivariable course
|By Corny (Corny) on Monday, May 24, 2004 - 09:43 pm: Edit
Believe me, we've all been there and we completely sympathize. I don't know how many times I couldn't understand a professor because english was not his or her native tongue. The worst is when you ask them to repeat something and you still can't understand.
My other pet peeve: why the hell can't math and physics professors stick to using a few greek letters that everybody knows (alpha, beta, gamma, delta, psi, phi). Xi and See are NOT easy to draw without practice so I end up with notes that look like wavy line doodling.
|By Corny (Corny) on Monday, May 24, 2004 - 09:56 pm: Edit
I just checked Berkeley's Math H53/H54 website. The books those classes use are the standard second year multivariable calc/linear algebra books (not necessarily books for math majors).
Math 25 tends to use third-year level books used by math majors like Principles of Mathematical Analysis by Rudin. The proofs in that book are harder just because of the amount of math background it assumes the student has. I just checked the Math 25 website and they're using a graduate-level textbook Real and Functional Analysis by Lang.
So the Berkeley honors courses H53/H54 are not equivalent.
|By Irock1ce (Irock1ce) on Thursday, May 27, 2004 - 12:07 am: Edit
eh. i know. but im just saying that the amount of cutthroat asians from china, japan and korea in there makes it 100000000 times harder.. for example... i know some students that came here as china's elite math program.. (we're talking finishing high school when they're 10) and they are just simply amazing in math... the tihng is.. most of these kids end up at UC Berkeley... UCB is cheaper, closer to home and more famous (in Asia) for engineering. Thats what i meant by math 53/54H being super hard.
|By Corny (Corny) on Thursday, May 27, 2004 - 09:43 pm: Edit
I guess it depends on the class. Some math classes don't grade on a curve so there isn't that much competition. But, you're right, if there is a curve, any class with super smart people would be extremely hard--no matter what the topic.
|By Norm (Norm) on Friday, May 28, 2004 - 04:33 pm: Edit
Irock1ce, cutthroat asians compared to IMO participants...hmm I think 55 has much smarter people that could take any of the people in H53/54 anytime.
|By Irock1ce (Irock1ce) on Saturday, May 29, 2004 - 02:39 am: Edit
oh u just dont know cutthroat Asians do you? As i said, there are the creme of the crop asian math geniuses here.... (btw, im pretty sure that Taiwan, China, Japan or South Korea could all kick our asses in Math). But if you dont believe me, you should come over here and check it out. UCB is cheaper, and its in a more convenient location. Thats why it attracts a good amount of Asian Math geniuses.
|By Irock1ce (Irock1ce) on Saturday, May 29, 2004 - 02:48 am: Edit
heres an interesting stat: in 2001, all 6 of China's IMO members won gold. Same in 2002. 2003, 5/6 won gold. 6th one won silver. This is #1 in the world. Another thing.. I actually know 2 former IMO gold medalists from China (well my dad does.. he fixes their car. they're doin their graduate studies right now.. one of them did undergrad here. other one at XingHua(china's MIT).
So, you can take math with Chinese IMO team... or U.S. IMO team... Chinese IMO team > U.S. IMO team. Thats one way that Math 53/54H could be super super tough. Have random asian people come over and turn your curve super hard (UCB doesnt have grade inflation either.).
|By Norm (Norm) on Saturday, May 29, 2004 - 11:49 am: Edit
Most Chinese IMO team doesn't go to UCB. More IMO students have gone to Harvard, or MIT, than UCB. Besides, if UCB top students are better than Harvard's top students, why don't I see them EVER beating Harvard in Putnam...
|By Irock1ce (Irock1ce) on Saturday, May 29, 2004 - 03:00 pm: Edit
lol yeah i know. im just saying random stuff. but im just saying that i have known chinese IMO people at UCB.
|By Vecter (Vecter) on Saturday, May 29, 2004 - 05:18 pm: Edit
on average, Chinese IMO > USA IMO,
but in 2001 USA got 2 perfect scores (Gabe Carroll @ Harvard and Reid Barton @ MIT) and so did China
|By Norm (Norm) on Saturday, May 29, 2004 - 05:59 pm: Edit
of course it is...they have a billion people to choose from.
|By Godis (Godis) on Sunday, May 30, 2004 - 02:39 am: Edit
not necessarily. the laws that limit families to having one children reduce the number of high school kids.
|By Irock1ce (Irock1ce) on Sunday, May 30, 2004 - 01:29 pm: Edit
yeah nowadays its a bit different. they have one billion people to choose from... if you count the old, the middle aged, the babies and everyone else. Sure. But wouldnt it make sense that a place like India would be #1 since they have no birth control laws and its next generation probably outnumber the next generation of chinese?
|By Vecter (Vecter) on Sunday, May 30, 2004 - 02:35 pm: Edit
Chinese people just accelerate their children in math
what's considered "accelerated" here in the US is standard in China
|By Norm (Norm) on Sunday, May 30, 2004 - 03:01 pm: Edit
china has tons of special programs geared specifically toward the IMO. We realize the IMO isn't life...we win anyway.
|By Scorpsjl (Scorpsjl) on Monday, May 31, 2004 - 01:43 pm: Edit
yea i agree with those last 2 posts, in a lot of different endeavors, there is an intersting pattern when comparing the west (usually the US) and the east (often china, and japan),. Japan and China tend to be superior at younger ages, to reach certain levels faster, and to be better trained/more disciplined at things. However, at higher levels, i.e. the professional level, etc, the US often wins, showing greater levels of creativity and risk taking, all importnat things for novel discoveries. THe same comment has been often made about baseball to explain why Japanese little-leaguers kick our ass, but why professional japanese players are nowhere near as gooda as ours. At the little league level, japanese-style is more honed and thus beats our kids. However, at the highest levels, the American MLB'ers can figure out the japanese style and beat them, and show more originality/creativity on the field. Of course these are all generalizaitons and not always true, but they make sense. In other words, china might do better at IMO than us without indicating that they are better than us at math. As vecter pointed out before i think, some really good US math students don't even do IMO. They are more intersted in researching, even at the high school level.
|By Rtkysg (Rtkysg) on Monday, May 31, 2004 - 02:57 pm: Edit
I am inclined to agree with you, however I think you need to limit this 'Western adult trophy' only to pure science and sports. The reason why many of the chinese/korean IMO kids are not so famous in mathematics is because many of them knows that math field is not productive (in term of money) and hence they would often go for Engineering and Business and leave all those weird math stuff.
Many of them join the competition just for the sake to get scholarship to a prestigious university in US and have a bright promising career afterwards.
In case of sports, a good US baseball player is much much much wealthier than a top-notch Japanese player. Sports, frankly speaking, is not as highly respected as academics in Asia, and hence less people commit themselves to become a pro.
I believe in term of trading and business, the chinese/japanese/korean professionals will be as good as the western ones
|By 301aish (301aish) on Wednesday, June 02, 2004 - 12:50 am: Edit
Why does eveyone make such a big deal about Math Team...i'm on math team, and once you've seen a certain question type enough times it's just reflexive and not really a matter of skill...isn't "outside the box" thinking actually tested much better in doing actual resarch...Things like USAMO and AIME are so arbitrary...the only people I know who have been able to do both with success are Joel Louis (The MAN!) and Gabe Carrol
|By Rtkysg (Rtkysg) on Wednesday, June 02, 2004 - 07:31 am: Edit
301aish, I agree with you, but Putnam is an exception i guess ...
|By Vecter (Vecter) on Wednesday, June 02, 2004 - 08:39 pm: Edit
301aish i miss your point.
how are AIME and USAMO arbitrary? People who do well on these (and then advance to MOP/IMO) often do great on Putnam also, not to mention college math in general...
you make it sound so easy ("reflexive"), but unless you can actually do it and make MOP/IMO (are you?? that would be VERY impressive), i wouldn't talk it down. I know that I certainly can't do AIME/USAMO, but I don't dismiss them as foolish just because I'm not good enough for them.
|By Pimpdaddy (Pimpdaddy) on Wednesday, June 02, 2004 - 10:46 pm: Edit
"Joel Louis"
wow, small world
|By Vecter (Vecter) on Wednesday, June 02, 2004 - 11:25 pm: Edit
I thought it was "Joel Lewis" (stuyvesant?)
|By 301aish (301aish) on Wednesday, June 02, 2004 - 11:38 pm: Edit
My big "point" (not trying to be arrogant) is that I don't see the big deal with these "geniuses" from Bulgaria, China, or whatever (although they are all VERY smart) I mean, they have been doing this stuff for years more than their American counterparts...It doesn't make them smarter, it just means that they've seen these problems dozens of more times and practiced, practiced, practiced. At that point, it becomes less intelligence and more test prep, albeit at a very high level.
At the same time, can you prepare like this for math/physics/biology research? of cousse, your dad or mom can be a doctor, but at some point you have to understand it for yourself, and make your own connections
Also, isn't the impact that research has more important than isolated math questions that don't have context?
|By 301aish (301aish) on Wednesday, June 02, 2004 - 11:38 pm: Edit
Pimpdaddy: You know Joel? From where? why "small world?"
|By Vecter (Vecter) on Thursday, June 03, 2004 - 01:22 pm: Edit
301, i think that getting a gold at IMO DOES mean that you're "smarter" (however that relative clause is used...).
have you seen Gabe Carroll's writing? I was browsing his website and looked on his "thoughts on harvard" and omg I could tell by reading his few sentences that his level of intellect was vastly superior to most people's i've seen. his language is so abstract and almost beautiful, just a reflection of the thought processes he learned through his math studies.
and remember that math is the foundation for most sciences. Try writing a scientific paper without manipulating numbers.
also, showing your proficiency in math proves that you're capable of learning basically anything you want to. Michael Lander (MIT prof, MacArthur fellowship winner, IMO gold, Westinghouse STS 1st place winner) basically ran the human genome project @ the whitehead institute. Math prodigy gone to bio.
sorry i guess i'm ranting, but my point is these math geniuses had to work for their skills ("natural" prodigies like Gauss aside) and spend countless hours studying writing doing working etc. while you and I were hanging out w/friends or focusing on something different (say research!). Being success in a math competition (or any competition for that matter) just shows that you're capable, so it's not fair to downplay USAMO/MOP/IMO. Saying that doing well in math is reflexive is the same as saying that doing well in the national biology olympiad is reflexive. of course! but you had to spend years learning all that "reflexive" stuff!
And doing well in research? Well that's a combination of luck, intelligence, and innovation. Like you said, you can't prepare per se for research, but you can in the sense that the more you know, the more you can possibly do. How can you possibly expect to do an advanced physics project if you don't know the math to handle maxwell's equations?
As an aside, I don't think that AIME/USAMO are arbitrary--people who REALLY know math do well on them consistently year after year. Of course you can get lucky.
|By Rtkysg (Rtkysg) on Saturday, June 05, 2004 - 01:22 am: Edit
It is true that AIME/USAMO is not arbitrary, but for those already in the field (Engineers, Scientist, Prof) it doesn't look as great anymore. The reason because in your college year, and even more in graduate school, many of these AIME/USAMO/IMO competitors does not exhibit better capability.
An easy illustration would be like this, John Nash try to compete in Putnam (Putnam by far is harder than AIME/USAM/IMO/IPhO/etc) 2 times and lost. Richard Feynman was a Putnam 1st winner. However, John Nash produce a brilliant Math Game Theory at the age of 22 (and yet still cannot win the Putnam). Feynman, get intimidated by abstract math at graduate school, and choose to go to Physics (he's definitely no less smart ).
Now would you judge John Nash is less smart than Feynman in Math ?? No. Nash > Feynman in mathematics. So don't get humbled by your incapability of doing USAMO/AIME. It does not mean you have a less great potential capability. It's just that you are not well-trained for that kind of competition. That's all no big deal
|By Buckojack (Buckojack) on Saturday, June 05, 2004 - 02:46 am: Edit
I don't know what the hell any of you are talking about with the math 55/53 /54/ h/24/25325//325/235235/32325, but as for the baseball thing, American's are better at baseball then the Japanese simply because our people on average are much bigger and stronger. Hideki Matsui was considered to be an enormous player in Japan, and he is simply average compared to American sluggers.
|By Vecter (Vecter) on Saturday, June 05, 2004 - 04:26 pm: Edit
I believe Nash got honorable mentions, which is still very respectable. I didn't know about Feynmann, but in hindsight it's not too surprising (hey, they both went on to win nobels!).
I understand you're point about not looking too far up on MOP/IMO people, but I was just replying to 301 that at the same time, they should not simply be dismissed.
ahh I just wish I were good @ math...
|By Aycaramba799 (Aycaramba799) on Saturday, June 05, 2004 - 11:28 pm: Edit
As impressed as I am with math geniuses, i think there is a certain level of unfairness. I think a great number of people could be amazing at those competitions if they were taught "competition math" at a young age. By that I mean, going into several of these competitions with the algorithms under your fingers helps alot.
For someone like me, who is an ok math guy, but not amazing, I would have loved to have the oppurtunity to distinguish my self in something that im actually good at, like history or english. Unfourtanetly, there are no real competitions that recognize those students (cept for maybe history day).
pardon my rambling
|By 301aish (301aish) on Sunday, June 06, 2004 - 07:35 pm: Edit
Vecter: do you get my drift now?
|By Vecter (Vecter) on Sunday, June 06, 2004 - 09:42 pm: Edit
sorta, it just seems like you were casting off the math geniuses as "reflexive", which I thought was an unfair assesment that took away from their accomplishments.
|By 301aish (301aish) on Monday, June 07, 2004 - 09:33 pm: Edit
For example, some of my friends just got back from ARML. One of them was like "i missed a medal because i wrote '64' instead of '64i' as the answer." Who cares if you had a moment of forgetfullness and wrote down the wrong thing--that's just like the SAT's--things like that don't happen in research. It's not petty and stupid in that sense. In research you have time to look over what you have done and THINK, not just spit out answers to randomly assigned questions of increasing difficulty. As a great math team coach and math teacher once told me, "It is always preferable to write your own problems than solve someone else's." I think that is the crux of the matter. Math team can SOMETIMEs (Not always) be people who are smart but like their challanges in recognizable, bite sized dosages. In that sense, they are more like puzzles, which are fun but ultimately , what is their point? That is the exact reason why i don't think math team is reflective of "math skills" and people who are good at math team are "geniuses." What are they really demonstrating in the end? This is very unlike the kind of abstract thinking and reasoning, and teamwork, that is necessary in a real research project. Kind of ranting here. Math team people, please don't be offended
|By Z00b (Z00b) on Tuesday, June 08, 2004 - 12:57 am: Edit
Heh, just read an interview with Bill Gates somewhere... I can't exactly recall... I think it might have been Forbes, The Week or PC Magazine and he was asked something like "I was always told that no matter how smart you are, there is always someone smarter than you. How do you feel about that? He referenced Math 55, saying everyone had 800s on their Sats and 5 on their APs, saying it gave him a reality check. Let me see if I can find it...
|By Vecter (Vecter) on Tuesday, June 08, 2004 - 04:07 am: Edit
Z00b I remember that also, I think it was BusinessWeek.
Yeah, he was asked about smart people and he said something along the lines of "There was this one class Math 55..." yada yada yada. I didn't realize Bill Gates was a math genius until then.
|By Mattlord (Mattlord) on Friday, June 18, 2004 - 03:19 am: Edit
what's gabe carroll's website?
|By Vecter (Vecter) on Friday, June 18, 2004 - 10:53 am: Edit
5 seconds on google answers questions faster than almost any forum can ;)
|By 2bad4u (2bad4u) on Sunday, June 20, 2004 - 03:00 pm: Edit
USAMO people are a million times more talented than 800M or 1600 , although at times it is true exposing oneself to competition math is part of doing great, I would hold more respect for someone who got honorable mention in putnam's without ever being exposed to comp math than someone who has been around it all their life and only gets in the top 5-20 in putnam
|By Serdu (Serdu) on Sunday, July 18, 2004 - 07:39 pm: Edit
One of my classmates (08'er) will go directly into Math 55 this fall. He is a math genius though. He was telling me about how he's already finished last year's problem sets.
|By Mruncleramos (Mruncleramos) on Wednesday, July 28, 2004 - 02:12 pm: Edit
I agree with Scorpsjl.
The topics covered in Math 55 are not really that hard... They use Principles of Mathematical Analysis by Walter Rudin and some other linear algebra book. I've finished the principles of mathematical analysis book and I can understand why even some extremely talented competition mathematicians would falter on the material. I don't consider myself a genius. I'm just another sophmore who finished Calc BC. In addition to that my competition math is mediocre. But all that the book really requires is hard work and some mathematical intuitiveness. On the other hand, doing well in the class requires alot of hard work. Honestly, they don't cover that many topics as it may seem.
|By Ali_Liu (Ali_Liu) on Thursday, July 29, 2004 - 05:58 pm: Edit
Does anyone know how IB Further Math compares to these courses?
|By Mruncleramos (Mruncleramos) on Friday, July 30, 2004 - 06:08 pm: Edit
IB Further Math barely pales in comparison to Math 55. It also is no match for Math 25 many other classes. IB Further Math is a toned down Introductory Analysis Course with other topics.
|By The_Brain9 (The_Brain9) on Saturday, August 07, 2004 - 02:51 am: Edit
What book would one use to become proficient enough at writing proofs to take Math 55? I am student who has done very well in calculus (easy 5 on BC) however, my school did not offer anything in the way of proofs. I have already checked out the website: http://www.artofproblemsolving.com/ so is there anything else? Any help is greatly appreciated and no I don't need anybody saying just to give up because it's too hard. Thanks.
|By Corny (Corny) on Saturday, August 07, 2004 - 10:45 am: Edit
Since you got a 5 on BC, you should get a book on calculus that is proof-based and work through the proofs. Make sure you understand the thought process.
One unusually good book (usually used in honors single variable calc courses) is
Calculus by Michael Spivak
Make sure to get the solutions manual for detailed explanation of proofs in the exercises.
Answer Book for Calculus by Michael Spivak
Look on Amazon to see the reviews. Yes, Math 55 will be much harder but at least you will have practice with writing proofs.
|By The_Brain9 (The_Brain9) on Saturday, August 07, 2004 - 12:20 pm: Edit
Corny, it's funny that you mention that book because I have it - I just haven't started working through it yet. Yeah, I picked it up because of the good reviews on Amazon...
Edit: I also have the solutions manual too!
|By Ubercollegeman (Ubercollegeman) on Saturday, August 07, 2004 - 04:03 pm: Edit
Spivak's Calculus is one of the best I've ever seen. It is a newer text than most of the classics by the masters, so the notation and stuff is all good, and I highly recommend it too.
It is rather difficult though. Don't be surprised if you can't do many of his problems.
If you think Spivak's book is too easy for you (highly unlikely, I think Spivak is only suited for the top 0.5% of high school math students if even that), I can recommend others that are even harder.
|By The_Brain9 (The_Brain9) on Saturday, August 07, 2004 - 05:44 pm: Edit
Ubercollegeman, Spivak is the perfect difficulty right now however I do want to hear some of your recommendations because Spivak doens't go into multi-var proofs.....
|By Mruncleramos (Mruncleramos) on Saturday, August 07, 2004 - 08:16 pm: Edit
Holy crap, how many people here can do Spivak's Calculus on Manifolds... I was underestimating you guys, that book is pretty terse. I would recommend Analysis on Manifolds or Rudin's Principles of Mathematical Analysis. If you work through them line by line and don't get frustrated.
|By Ubercollegeman (Ubercollegeman) on Saturday, August 07, 2004 - 09:16 pm: Edit
Not Spivak's Calculus on Manifolds. Just Spivak's Calculus. He has two books.
Some books that are a bit harder or about the same as Spivak's are:
Apostol - Calculus Vols. I and II (I is single-variable, II is multivariable + other stuff)
Courant - Differential and Integral Calculus Vols. I and II (see above note about Apostol)
Hardy - A Course of Pure Mathematics (no multivariable or beyond)*
*: This book is especially difficult, and Hardy was one of the greatest mathematicians of the 20th century (and arguably when combined with Littlewood the greatest mathematical team ever). The book is written very clearly, yet "rigor" cannot be overstated. If you want to take mathematics seriously, start with this book.
Books to avoid are basically any main-stream types like Stewart's, Thomas', and Larson's that have reduced calculus to a system of plugging and chugging. No beauty can be found in those books.
WARNING: I would look at Spivak's more closely. If Spivak's is "just right" for you, I would work with that a little bit before jumping into Hardy's. That book is a classic among classics for a reason: it may be the most difficult elementary calculus book ever written.
Also note that if you want books that match the AP curriculum, don't look into these. These are far more difficult than anything the AP test can offer, and the topics get far more abstruse.
|By Corny (Corny) on Sunday, August 08, 2004 - 12:27 am: Edit
Spivak's Calculus is a superb book so you definitely made a good choice.
I hesitated mentioning Apostol's book just because I've heard there aren't as many detailed explanations of the proofs and at this stage you need to understand the underlying thought process. I haven't read Hardy so I can't comment on that one.
Believe me, you don't need to have studied multivar calc beforehand. The proof writing process is the most important thing right now. Once you get that down pat, any new topic will be relatively easy.
If, however, you're looking for a proof-based multivar calc book, there is Vector Calculus, Linear Algebra and Differential Forms by John H. Hubbard. But it is difficult and probably would be helpful once you're in Math 55. It is probably the best example of the type of proofs Math 55 will deal with.
|By The_Brain9 (The_Brain9) on Sunday, August 08, 2004 - 02:03 am: Edit
Thanks for all of your responses. I did about 3 hours of Spivak's Calculus today and hopefully will go cover to cover. I got to get some sleep right now but please - if anybody has any recommendations for intro proof based mathematics - I am willing to listen. Goodnight!
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