CSC165 — Content

Lecture Summaries

Lecture 1 Summary.

Lecture 2 covered roughly Section 2.1 of the Course Notes below; Additional commentary.

Lectures 3–5 covered the rest of Chapter 2 of the Course Notes below; Additional commentary.

Statement forms up to and including Fri Sep 18.

Introduction to multiple quantifiers.

Examples of understanding symbolic statements inside-out and by tracing.

Tutorial Exercises

1, 2, 3, 4.

Course Notes

These are based on my original notes for the design of CSC165, formatted with some additions by various instructors.

Chapter 1.

Chapter 2.

Chapter 3: sections 3.1–3.7, the meaning of 3.8–3.15 (much of it has become too abstract/symbolic), and 3.16–3.17 were covered.

Chapter 4: proof; thinking about proving statements is also a valuable way to understand them (and vice versa).

References

There are some good logic, proof and reasoning books, except none is quite a good fit for CSC 165: 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, and many are expensive.

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.

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.