What is the role of a teacher (of mathematics) at university?
I'm a student. I have always wanted to be a researcher/scientist cum professor all my life. The following are the qualities I would like to be instilled in me (and a few which didn't turn out the way I expected from a teacher) as a teacher at a university level. Note that some of the points are applicable for teachers in general and some specifically for math teachers.

(The following are in no order of preference)


One of the most important things that a teacher must do is to use the blackboard and more than you use a powerpoint. There is some kind of magic related to using the board for math. One of my professors used to use powerpoints for his classes, and most of the time students (including me) fell asleep.
If in case you do want or have to use powerpoints, then make sure to create animations like the ones here. One of the fascinating things about those animations is how perfectly it fits to capture a person's attention.
Encourage students to use online resources like OCW MIT. When I was in my university (graduated this year), neither did I have internet connection, nor was I aware of such a resource online. Encourage and suggest MOOCs from Coursera, edX, etc. which might be relevant to your course. It is not necessary that they should register/complete every single course or resource. Give them two or three options and ask them to pick one.
Make it an active class. And make it fun too. I learnt a lot from Gilbert Strang and Mehran Sahami. Be enthusiastic in class, that will help students get out of their tiredness. You can also toss out chocolates like Sahami does when students answer/ask questions.
Solve problems in class - either all types of the same level (easy/medium/hard) or one type with all the levels, going from the easiest to the hardest. The point is to make sure they understand the problem solving process. In addition, solve example problems from the textbook or handout and for every example problem, give them a problem to solve either in class or as an ungraded homework. This makes sure they are actually doing something in a math class rather than just trying to consume the knowledge passively.
Make sure the subject you're taking can be related to other majors and fields. Most of the technical subjects have some variation of mathematics being used in them. Take Calculus. It is used everywhere, even when we think we don't need it. I always thought it was used only in continuous domains, mostly in physics and not at all in any other fields. I was mistaken. You don't have to make this a mainstream for your class. Maybe as an ungraded homework or just a casual mention when the relevant topic comes up is enough to keep the spark up.
Go a bit beyond the syllabus. I know this will be hard, but, just a bit will be enough. It may involve deeper concepts, real world applications, etc. That is up to you to choose. Personally, I have always found it beneficial for me to learn a bit more than what is needed so that I won't be caught off guard during exams. This also helps students if they wished to pursue higher levels of the course possibly leading to research.
Have a review class before exams. Walter Lewin's lectures had reviews for midterm and the finals. It sort of helps to review everything in class rather than spending extra time apart from the newer material to be learnt the day before exams.
Inform students exactly how many hours they'd need to spend on an avg outside class. I wound up with terrible time management because I had no idea how to allot the required time for each course. This led me to focus on subjects I loved and got better grades and subjects I didn't find interesting for which I didn't spend time - and I flunked in them. Huge mistake.
Use standard textbooks, especially the ones which have 4 and above ratings on amazon. Ask students if they liked a different textbook, and if it is a better suited one, then switch. Don't use textbooks which you find personally attractive.
If it is not a problem with your university rules, make sure attendance isn't compulsory. There will be at least one or two students who might find attending lectures boring. To counter that effect, make sure you deliver incredible lectures that makes students feel want to attend rather than have to attend. In my university 80% was mandatory and I found it a huge waste of time for most of my classes.
Make sure problem sets contain all levels of problems. It helps students to practice properly. This increases confidence. In addition, don't pick problems from the prescribed textbook. Just pick another textbook and give them the problems to solve. For math, I'm sure there are numerous books and resources online.
Identify the distribution of students in your class. There will be one/two/a few gifted students in your class. Maybe conduct a simple quiz at the end of week 1 or 2 to find out who they are. (I find it hard to explain it in words) As a teacher, you will know who these people are. Now, chances are that they might be bored if the class feels too easy. In this case, add extension problems which are very very challenging. These can be ungraded, but interesting to solve. These gifted students will always go out of their way to solve them. This ensures that their skills don't rust away with time. Another horrible experience of mine.
Rehearse for every class you take, fully. Practice. If it is a 50 min lecture, give a 50 min lecture to the empty hall. Walter Lewin used to do this for every lecture he gave (he quoted in an interview somewhere on OCW or YouTube, not sure where).


These are the ones off the top of my head. Hopefully, these are enough.