Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics.

Ongoing course

**Time:** MWF 02:30 PM – 03:20 PM**Location:** Zoom (First two weeks) – ECCR 131**Office hours:** Click here

Grading

**Homework:** 25% – Weekly homework (you must turn them in)**Midterm I (02/18 ): ** 20% **(Please check canvas!)****Midterm II (04/01):** 25%**Final (05/01) :** 30%

Homework sets

**Assignment 10 (Due to 04/25)****Chapter 11****Section 11.2** 3,13,15,16**Section 11.3** 1,7

**Assignment 9 (Due to 04/21)****Chapter 10: **

4,6,8,24,37

**Assignment 8 (due to 04/11)****Chapter 7**

1,9,12**Chapter 8**

6,7,21

**Assignment 7 (due to 04/01)****Chapter 4**

12, 14, 18**Chapter 5**

A.12, B.17**Chapter 6**

A.4, B.13, B.16

**Assignment 6 (due to 03/14)****Chapter 4:** 3, 6, 7, 12, 14, 24

**Assignment 5 (due to 03/07)****Section 3.2:** 6**Section 3.3:** 10**Section 3.4:** 4, 17**Section 3.5:** 12, 15, 19**Section 3.7:** 13**Section 3.9:** 3, 5**Section 3.10:** 1, 3, 5

**Assignment 4 (Due to 02/11)****Section 2.7:** 1-10**Section 2.10:** 1-12

**Assignment 3 – due to** 02/04**Section 1.8** 4.a,4.b, 5.a, 5.b, 12**Section 2.1** 1-15**Section 2.2** 1-14

**Assignment 2 – due to Jan 28th****Section 1.2:** A.1.f, A.2.5, B.15, B.19**Section 1.3:** A.1, A.6, C.14**Section 1.5:** 1.a, 1.b, 1.c, 1.i, 5, 8**Section 1.6:** 2.a, 2.f, 2.g**Section 1.7:** 11,12,13,14

**Assignment 1 – due to Jan 21st.****Exercises for Section 1.1**

A.7, A.14, B.25, B.27, C.32, C.38, D.39, D.45, D.48

*All problems refer to our textbook*

Textbook

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Course notes

## Final Review – MATH 2001

General comments on the final. Review of some of the main concepts.

## Composition of Functions – MATH 2001

More on properties of functions. Composition of functions.

## Functions – MATH 2001

More on integers modulo n. Relations between sets, functions as relations, injective, surjective functions.

## Integers modulo n – MATH 2001

A warm up with equivalence relations and introduction to integers modulo n.

## Relations – MATH 2001

Introduction to relations, properties of relations, equivalence relations and equivalence classes.

## The Fundamental Theorem of Arithmetic – MATH 2001

Using induction to proof theorems involving graphs. Proof by smallest counterexample and the Fundamental Theorem of Arithmetic.

## If and only Proofs and Sets – MATH 2001

How to prove if and only if theorems, proofs involving sets and more.

## Midterm II – Recap – Part II – MATH 2001

Set of problems to practice some proof techniques.

## Congruence of Integers – MATH 2001

Using DeMorgan’s Law to give contrapositive proofs. Congruence of Integers.

## Using cases and Contrapositive Proof – MATH 2001

Proving theorems by considering cases. Contrapositive Proof.

## Direct Proof – MATH 2001

Definitions, theorems and lemmas. How to prove conditional statements? Direct proof.

## Inclusion-Exclusion Formula and Pigeonhole Principle – MATH 2001

Inclusion-Exclusion Formula and Pigeonhole Principle.

## Permutations with indistinguishable objects – MATH 2001

Number of integer solutions for equations and Permutations involving indistinguishable objects

## Permutations and Combinations – MATH 2001

Factorials, permutations, combinations and gamma function

## Addition and Subtraction Principles – MATH 2001

Using the addition and subtraction principle to count lists.

## Multiplication Principle – MATH 2001

Lists, counting lists and the multiplication principle

## Logical Equivalence, Quantifiers and Negation – MATH 2001

Logically Equivalent statements, use of quantifiers and how to negate a statement

## Conditional and Biconditional Statements – MATH 2001

Sufficient conditions and necessary and sufficient conditions.

## AND, OR, NOT – MATH 2001

Combining statements to form new ones: AND, OR. And negation of a statement.

## ZFC, logic and statements – MATH 2001

Zermelo-Fraenkel axioms, set-theoretic definition of the natural numbers, logic and statements.

## Indexed Sets and the Russell’s Paradox – MATH 2001

Indexed Sets, union, intersection of indexed sets, sigma and Pi notation. A discussion of the Russell’s Paradox.

## Set operations and Venn Diagrams – MATH 2001

Generating sets from others: Union, Intersection, Difference and Complement. Representing sets with diagrams.

## Power Sets and Cartesian Product of Sets – MATH 2001

Generating sets from others: Power set of a set and Cartesian Product of sets.

## Infinite Sets – MATH 2001

Some paradoxes involving infinite sets and the Cantor’s diagonal argument.