CSC 165: Lectures

Week		Topics	Covers	Notes
1	Sept 11	Course Introduction universals and implication		Warm-up puzzles Chapter 1 (PS)
2	Sept 18	Sentences, statements, symbolic notation, and implications		Chapter 2 (PS)
3	Sept 25	Quantifying implication, equivalence, existential quantification		Chapter 3 (PS) [updated 11 October]
4	Oct 2	Manipulating quantifiers, conjunction, disjunction, and negation
5	Oct 9	Formal proofs	4.2-4.5	No class Monday due to Thanksgiving holiday Chapter 4 (PS) [old version, only first half]
6	Oct 16	Basic proof structure	4.1, 4.6-7	Term Test 1 on Monday
7	Oct 23	Other proof structures	4.9-4.19	Chapter 4 (PS) [updated 27 Oct] Gary Baumgartner's summary of proof structure
8	Oct 30	Binary notation, analyzing algorithms	4.14, 5.1	Chapter 5 (PS)
9	Nov 6	Big-O notation	5.2, 5.3
10	Nov 13	Asymptotic notation and time complexity	5.3, Ch.6	Chapter 6 (PS)
11	Nov 20	Bounding running time of programs, floating point systems	Ch.6, 7.1	Term Test 2 on Monday
12	Nov 27	Error in numerical methods	7.2-7.3	Chapter 7 (PS)
13	Dec 4	Handling error, review	7.4-7.7

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

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 [updated 11 Oct]
Chapter 4 (PS): Proofs [updated 27 Oct]
Chapter 5 (PS): Analyzing Algorithms [added exercises 8 Nov]
Chapter 6 (PS): Running time of programs
Chapter 7 (PS): Numerical Systems [updated 29 Nov]

Many of the lecture notes included here are adapted from other sources, including Gary Baumgartner and Danny Heap's CSC 165 notes, the textbook, 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.