MAT 215

Introduction to Mathematical Reasoning

Lynn Narasimhan

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Welcome to Math 215:  Introduction to Mathematical Reasoning!

This course is about the activity of doing mathematics. In the course, we'll explore the logic and language of mathematics as well as some of the fundamental concepts concerning numbers, sets, relations, and functions.   Through this process, we'll study the role and nature of proof in mathematics. We'll work through most of chapters 1-6 in the assigned textbook Proofs and Fundamentals.

The course should help you achieve the following objectives:

•appreciate the role of logic and exploration in mathematics.

•review and study some basic concepts about numbers, sets, relations, and functions which will be used in later math classes.

•learn how to use the language and symbols of mathematics to express statements precisely.

•gain experience in explaining and communicating your ideas, both informally and formally, orally and in writing.

•increase your awareness of the power of abstraction.

Here is a rough outline of this course (subject to change):

Week 1 Introduction; informal logic
Week 2 Strategies for proofs
Week 3 Sets
Week 4 More sets;
Week 5 Test 1,  Functions
Week 6 More functions
Week 7 Equivalence relations
Week 8 Relations; Test 2
Week 9 Infinite sets
Week 10 Mathematical induction
Week 11 Final exam