Intro. to Discrete Mathematics – MATH 2001

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

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

Book of Proof – Third Edition

by Richard Hammack

Other books I like

by Sheldon Ross

by Henk Tijms

Course notes

Final Review – Part II – MATH 2001

Second part of the recap for the final.

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.

Strong Induction – MATH 2001

Strong induction.

Mathematical Induction – MATH 2001

Introduction to proofs by mathematical induction.

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.

More Examples of Direct Proof – MATH 2001

More examples of direct proofs!

Direct Proof – MATH 2001

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

Combinatorial Proof – MATH 2001

How to prove identities telling a story.

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

Midterm I – Recap – MATH 2001

Recap for first midterm

More on Combinations – MATH 2001

Problems involving combinations

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.

Sets – MATH 2001

Introduction to the first concepts of set theory.