**Course: MATH-UA 125 Introduction to Mathematical Proofs/ MTHED-UE 1049 Mathematical Proof and Proving**

**Course Description:** This course introduces elements of
mathematical
proof, focusing on three mains themes: 1. The meaning of mathematical
statements -- universal/existential; 2. The role of examples in
determining the validity of mathematical statements; 3. The various forms
and methods of mathematical proofs, including direct (deductive) proof;
proof by exhaustion; indirect proof (by contradiction, or by
contrapositive); mathematical induction; and disproof by counterexample.
This is a problem-based course. Lessons are structured around activities
that engage students in doing proofs that are meaningful to them and based
on mathematical topics with which they are familiar.

**Syllabus:** pdf

**Instructors:** Jalal Shatah and Orit Zaslavsky, shatah(at-sign)cims.nyu.edu, oz2(at-sign)nyu.edu

**Meeting Time/Location:** Monday 1145AM-2PM, (formerly KIMM 804)
changed to WWH 317

**TA:** Steven Heilman, heilman(at-sign)cims.nyu.edu

**TA Office Hours:** WWH 1108, Thursday, 11AM-1PM, or by
appointment

(If this time is bad for many people, let me know and I will make a change.)

**Recommended Textbooks:** Chartrand, Polimeni and Zhang,
__Mathematical Proofs: A
Transition to Advanced Mathematics__.

Fendel and Resek, __Foundations of Higher Mathematics:
Exploration and Proof__.

**Other Resources:** An
introduction to mathematical
arguments, Michael Hutchings

__An Introduction to Mathematical Proofs__, Jimmy Arnold.
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