Lecture Notes

This page gives highlights of past lectures and provides lecture notes, reading assignments, and exercises.

Chapters and sections in the readings are from the textbook, unless specified otherwise.


Dates Topics
Mar 04

Course introduction. Overview of course topics. Examples of mathematical thinking applied to number definitions and results.

Readings:

Mar 09
Mar 11

Propositional Logic. Connectives and truth tables.

Applications of propositional logics. Propositional equivalences.

Readings:

ENSINO REMOTO EMERGENCIAL starts here
Aug 03

Overview of Ensino Remoto Emergencial

Propositional Logic. Connectives and truth tables.

Applications of propositional logics.

Propositional equivalences. Satisfiability

Readings:
Aug 05
Aug 10

First-order logic (predicate logic). Predicates and quantifiers.

Nested quantifiers.

Readings:
Aug 12
Aug 14
Aug 17

Inference rules.

Readings:

Weekly Q&A


Fallacies.

Readings:
Aug 17
Aug 19

Proof methods.

Readings:
Suggested readings on automating proof production:

Weekly Q&A
Aug 26

Weekly Q&A
Sep 02
Sep 03
Sep 04 		Exam 1
Sep 09
Sep 14
Sep 16

Sets. Introduction and operations.


Functions. Sequences. Summations and product.


Readings:

Weekly Q&A
Sep 21
Sep 23

Cardinality and countability. Some countable sets. An uncountable one.

Readings:

Weekly Q&A
Sep 30

Weekly Q&A
Oct 05
Oct 07

Induction. Weak and strong induction.

Readings:
  • Induction class notes
  • Chapters 4.1, 4.2 (Rosen 6th Ed.)
Oct 14
Oct 17

Recursion and structurual induction. Recursive algorithms.

Readings:
  • Recursion class notes
  • Chapters 4.3, 4.4 (Rosen 6th Ed.)

Weekly Q&A
Oct 19
Oct 21

Binary representation of numbers. Abstract Boolean algebra. Representation of Boolean functions. Logic gates. Circuit minimization.

Readings:
  • Boolean algebra class notes
  • Chapters 11.1, 11.2, 11.3, 11.4 (Rosen 6th Ed.)

Weekly Q&A
Oct 29
Oct 30 		Exam 2
Nov 03
Nov 04 		Make-up Exam
Nov 06
Nov 07 		Special exam