typical car is driven about , miles per year if gasoline costs $ /gallonthen the yearly gas bill is $ for the less efficient car and $ for the more efficient car if we ignore issues such as the payback that would be received if we invested $ in bankit would take years to make up the difference in price at this pointthe buyer must decide if price is the only criterion and if -year payback time is acceptable naturallya person who drives more will make up the difference more quicklyand changes in gasoline prices will also greatly affect the outcome example when at the supermarket doing the week' shoppingcan you estimate about how much you will have to pay at the checkoutone simple way is to round the price of each item to the nearest dollarand add this value to mental running total as you put the item in your shopping cart this will likely give an answer within couple of dollars of the true total further reading most of the topics covered in this are considered part of discrete mathematics an introduction to this field is discrete mathematics with applications by susanna epp [epp an advanced treatment of many mathematical topics useful to computer scientists is concrete mathematicsa foundation for computer science by grahamknuthand patashnik [gkp see "technically speakingfrom the february issue of ieee spectrum [sel for discussion on the standard for indicating units of computer storage used in this book introduction to algorithms by udi manber [man makes extensive use of mathematical induction as technique for developing algorithms for more information on recursionsee thinking recursively by eric roberts [rob to learn recursion properlyit is worth your while to learn the programming language lispeven if you never intend to write lisp program in particularfriedman and felleisen' the little lisper [ff is designed to teach you how to think recursively as well as teach you lisp this book is entertaining reading as well good book on writing mathematical proofs is daniel solow' how to read and do proofs [sol to improve your general mathematical problem-solving abilitiessee the art and craft of problem solving by paul zeitz [zei zeitz