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Introduction to abstract mathematics: course

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1 Description

This is a one-semester course to introduce math majors into pure/abstract mathematics. It's mostly about proofs. However, I would like to introduce a few other things that will make linear algebra, advanced calculus, group theory, topology, etc easier to absorb later on.


  • Introduction to higher mathematics
  • Introduction to advanced mathematics
  • Introduction to proofs

2 Prerequisites

3 Outline

About proofs...

"Because I don’t have time to write you a short letter, I write you a long one." Attributed to Hemingway, Cicero, Voltaire, Mark Twain, Blaise Pascal, Goethe.

In writing proof we'd better follow the latter approach, especially when we are still learning.

"If you like laws and sausages, you should never watch either one being made." (Mis)attributed to Bismarck.

We'll have to watch, if we want to learn how to do it.

In addition to proofs we need to start to become familiar with various mathematical constructions. They should be illustrated with examples from previous courses (calculus and precalculus).

4 Review

5 Notes


6 Further reading