Math 2513 - 002 Discrete Mathematical Structures
- Office Hours: Held in1015PHSC. Mon 1:15pm-2:15pm; Tue 10am-11am; Thu 1pm-2pm, or by appointment.
- The primary textbook for the course is Mathematical Reasoning: Writing and Proof by Ted Sundstrom.
This is found on the American Institute of Mathematics approved open source mathematics textbook page.
There are other good discrete mathematics resources on the AIM page; check out the Introduction to Proofs section.
- Here is a direct link to the textbook.
- There is a series of Youtube screencast videos which accompany the textbook.
- Midterm I is held in class on Monday, September 8. It covers chapters 1 and 2 of the textbook (up through page 81).
I will hold a review for the midterm from 1pm to 2pm on Saturday, Sept 6 in PHSC 114.
- Midterm II is held in class on Monday, October 13. It covers chapters 3, 4 and 8 (sections 8.1 and 8.2) of the textbook.
I will hold a review for the midterm from 9:30am to 10:30am on Friday, Oct 10 in PHSC 117.
- Here is an old midterm that has good overlap with our place in the course (ignore the Schroeder Bernstein question).
- Midterm III is held in class on Monday, November 24. It covers the sections of the book on set theory, functions, bijections, and applications to group theory (in-class and online notes).
- Here are some old midterms which have some overlap with the sections on set theory, functions and some group theory. (Have a look at my old discrete math pages for more exam and quiz questions.) old midterm and solutions; another old midterm.
- Information Sheet
- Here are comments on Class Assignment 01.
- Comments on the class assignment for Sept 3.
- A handout on the Least Principle. This will change as the semester progresses!
- Midterm I solutions and a blank exam.
- Some material related to class group projects: proof using Division Algorithm and cases, properties of divides,
key properties of congruences, some tables (mod m), some divisibility criteria,
and some proofs by induction.
- More material: strong induction proofs, irrationality proofs, Least Principle induction style proof, and
a Flowchart of ideas for this section of the course.
- The Die Hard examples.
- Class handout on the uniqueness portion of the fundamental theorem.
- Euclid's Theorem on infinitely many primes, and the homework problem on infinitely many primes congruent to 3 (mod 4).
- Some group work examples on inclusion/exclusion and on the proof of inc/exc for three sets.
- Some group work examples on injective functions, inj/sur/bijective functions,
power sets, subsets,
and some examples of bijections among well known sets.
- Some class notes on group theory.
- More details on the proof of Cayley's Theorem.
- Properties of functions between groups that preserve multiplication.
- Some symmetry groups in 2-dimensions and in 3-dimensions. (some solutions to Hwk 14 problems).
- Explicit examples of subgroups and their left translates in Lagrange's Theorem.
- An explicit isomorphism of groups (solution to a Hwk 14 problem).
- Solutions to Hwk 15.
- Some equivalent sets.
- Some countable and uncountable sets.
- Some Schroeder-Bernstein applications.
- Solutions to Midterm III and to Midterm II.
- #01. Due Wed Aug 27. Pge 12: Q1; Pge 26: Q1a; Pge 27: Q2b, Q2c, Q5a.
- #02. Due Fri Aug 29. Pge 40: Q1, Q2; Pge 42: Q12; Pge 44: Q1, Q2.
- #03. Due Fri Sep 05. Pges 74-77: Q2(a,c,f), Q3(a,d, h), Q9, Q10.
- #04. Due Wed Sep 17. Hwk questions Q1 and Q2 from The Least Principle handout.
Textbook: Pge 90: (Progress Check 3.2) Q3. Pge 96: Q1(a), Q3(a), Q3(b). Pge 126: Q3(b), Q4, Q5(a).
- #05. Due Fri Sep 19. Pge 98: Q11(a)(b)(c), Q12(a)(b). Pge 138: Q5(a)(b)(c).
- #06. Due Wed Sep 24. Pge 138: Q6(a)(b), Q7, Q8. Pge 153: Q2(a)(b).
- #07. Due Fri Sep 26. Pge 152-156: Q6, Q7(a)(b), Q8(b), Q18, Q19.
- #08. Due Fri Oct 03. Pge 196: Q1(a,b,c), Q3, Q5, Q6, Q7.
- #09. Due Mon Oct 06. Pge 424-425: Q1(a,c,e), Q3(a,b), Q5(a,b,d,e), Q7(c,e).
- #10. Due Wed Oct 08. Pge 436-439: Q7(a,b,c), 14(a,b), 19(d).
- #11. Due Fri Oct 24. Pge 240-242: Q7(a,b), Q13(a,b,c,d). Pge 252: Q5(a,b,c). Pge 261: Q1(a,b,c,d,g,h), Q2(all parts), Q7(a,b).
- #12. Due Fri Oct 31. Pge 304: Q5, Q7, Q8. Pge 317-318: Q2(a,b), Q3(a,b,c,d), Q12.
- #13. Due Mon Nov 03. Pge 332-333: Q7(a,b,c,d), Q10(a,b). Pge 346-347: Q8(a,b,c,d,e).
- #14. Due Wed Nov 12. Do the following. They are based on these class notes.
- #15. Due Wed Nov 19. Do the following set. They are also based on these class notes.