CSC 165: Lectures

Week		Topics	Covers	Notes
1	Sept 10	Course Introduction Universals and implication	Ch.1	More funny headlines Puzzles are in the Ch.1 notes No tutorial this week
2	Sept 17	Sentences, statements, symbolic notation, and implications	Ch.2
3	Sept 24	Quantifying implication, equivalence, existential quantification	Ch.3
4	Oct 1	Manipulating quantifiers, conjunction, disjunction, and negation	Ch.3
5	Oct 8	Formal proofs	4.2-4.5	No class or tutorial Monday due to Thanksgiving holiday
6	Oct 15	Basic proof structure	4.1, 4.6-7
7	Oct 22	Other proof structures	4.9-4.19
8	Oct 29	Binary notation, analyzing algorithms	4.14, 5.1
9	Nov 5	Big-O notation	5.2, 5.3
10	Nov 12	Asymptotic notation and time complexity	5.3, Ch.6
11	Nov 19	Bounding running time of programs, floating point systems	Ch.6, 7.1
12	Nov 26	Error in numerical methods	7.2-7.3
13	Dec 3	Handling error, review	7.4-7.7

The "covers" section numbers above are from the online lecture notes.

Lecture schedule is provisional and subject to change as the term progresses. Please check back each week to confirm reading assignments.

Online lecture notes

These notes roughly correspond to material covered in lecture, sometimes in more detail and sometimes in less detail. Please let me know of any errors, typos, omissions, or things that should be added.

Chapter 1 (PS): Introduction
Chapter 2 (PS): Quantification and Implication
Chapter 3 (PS): Logical Connectives
Chapter 4 (PS): Proofs
Chapter 5 (PS): Analyzing Algorithms
Chapter 6 (PS): Correctness and running time of programs
Chapter 7 (PS): Numerical Systems

Many of the lecture notes included here are adapted from other sources, including Gary Baumgartner and Danny Heap's CSC 165 notes, the textbooks listed below, and Jim Hoover and Piotr Rudnicki's logic notes.

References

In the last few years a number of good logic, proof and reasoning books have been published. However the more formal ones tend to assume some mathematical sophistication, the less formal ones are not formal enough, and many have a lot of specific mathematics not relevant to this course (though often relevant to later CS courses). None make connections with programming. So none is a perfect fit.

We don't want you to spend a lot of money on a textbook you may not find useful. So browse the following to find any that are helpful to you. (Of course, just like in your programming courses, you must spend most of your time time thinking, doing and experimenting).

One very readable, informal and introductory book is:

How to Read and Do Proofs, Daniel Solow, Wiley.

A classic book on how to solve problems (and highly recommended to read sometime) is:

How to Solve It, G. Polya, Princeton Science Library

The following two books are a nice mix of formal and informal, and available on Short Term Loan at the Engineering and Computer Science Library:

Learning to Reason, Nancy Rodgers, Wiley.
Proof, Logic and Conjecture, Robert S. Wolf, W.H. Freeman and Company.

Two books which concentrate more on the formalization are:

Doing Mathematics, Steven Galovich, Saunders College Publishing.
Introduction to Mathematical Reasoning, Peter Eccles, Cambridge University Press.

Finally, the following book focuses on how mathematics is done:

An Accompaniment to Higher Mathematics, George R. Exner, Springer.