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.
Rodrigo Ribeiro 