A rigorous introduction to discrete mathematical structures, proof techniques, and programming. Topics include sets, functions, sequences, relations, induction, propositional and predicate logic, modular arithmetic, and mathematical programming.
The class meets TR 2:00 - 3:15 pm in Petty 303. The final exam is Saturday, December 10, 2016 at 3:30 am.
All announcements and handouts will be posted on Canvas. Be sure to check your UNCG email regularly.
The exercise list in the course notes on Canvas will be updated as the semester progresses.
Make sure the assignments you turn in are in compliance with the Homework Guidelines for Mathematics.
Tuesday, 8/23/2016: I gave out the syllabus and lectured on 1.1 and 1.2. I will do some more examples before moving on to 1.3 next time, but you should be able to complete most of the exercises in 1.1. and 1.2. Read 1.1-1.3 for Thursday. If you plan on using your laptop for the programming assignments, install Python 3.* from the The official home of the Python Programming Language, and bring your laptop to class.
Thursday, 8/25/2016: I finished 1.2, 1.3, and introduced the programming project. HW 1.1-1.3 are due on Tuesday. P0 is due Thursday. Be sure to keep up with due dates in Canvas. Read 1.4 for Tuesday.Tuesday, 8/30/2016: I lectured on 1.4 and started 1.7. I will continue 1.7 next time, leaving some time for P1. Read 1.7-1.8 for Thursday. If you plan on using your laptop for the programming assignments, install Python 3.* from the The official home of the Python Programming Language, and bring your laptop to class.
Thursday, 9/01/2016: I completed 1.7 and showed some Python to help with P1. The exercises are due Tuesday. I added a folder to the main Canvas page where I will put solutions and handouts. Read 2.1 for Tuesday.
Tuesday, 9/06/2016: I gave out a proofs sheet and introduced sets (2.1 and 2.2). I will finish 2.2 next time. Bring your laptop, as we will cover P2.
Thursday, 9/08/2016: I gave out a P2 and finished 2.2. I will collect 2.2 on Tuesday.
Tuesday, 9/13/2016: I finished 2.3. I will lecture on 2.4 on Thursday. If time permits, I will do some Python on Thursday as well. The homework 2.3 exercises are due Thursday. Read 2.4 for Thursday. I updated the shared folder with more HW solutions and a sample test. Test 1 is next Thursday.
Thursday, 9/13/2016: I almost finished 2.4. I will complete some proofs on Tuesday, then we will review for Test 1. Test 1 is next Thursday.
Tuesday, 9/20/2016: I did some proofs about summation and showed how to define functions in Python. Then we reviewed for Test 1.
Thursday, 9/22/2016: Test 1: average 77
Tuesday, 9/27/2016: I returned graded tests and covered 4.1 on divisibility and modular arithmetic.
Thursday, 9/29/2016: I finished 4.1 and covered most of 4.2. You should work on 4.2 exercises, but I will not collect them on Tuesday. On Tuesday, I will give the algorithm for fast exponentiation before moving on to 4.3.
Tuesday, 10/04/2016: We finished 4.2 looking at divisibility proofs. Then we went through the base b expansion and fast exponentiation algorithms in detail. Sample Python code can be found in the shared folder on Canvas in the file algorithms.py. I will collect 4.2 on Thursday. The programming assignment P4 can be submitted on Canvas. Read 4.3 for Thursday.
Thursday, 10/06/2016: I covered extended Euclidean algorithm and Bezout's theorem. I handed out P5. We are slipping a bit behind the schedule in the syllabus. Continue to remind me to push deadlines. Read 4.4 for Tuesday.
Tuesday, 10/11/2016: We covered solving linear congruences by computing modular inverses and Chinese Remainder Theorem. Complete 4.4 for Thursday. Read about crytpography 4.6 for Thursday.
Thursday, 10/13/2016: I covered RSA encryption and shift ciphers. I handed out P6 and an RSA worksheet. I will collect 4.6 and P6 on Thursday. There is no class on Tuesday because of Fall break. Read 5.1 for Thursday.
Thursday, 10/20/2016: I handed out an RSA problem and Test 2 study guide today. Both can be found in the shared folder on Canvas. I covered 5.1 on mathematical induction. I will collect 5.1 on Tuesday. Test 2 is on Thursday, so Tuesday is a review day if you come in with questions.
Tuesday, 10/25/2016: Review for Test 2. Be sure to bring a calculator that can do arithmetic with 8 digit numbers.
Thursday, 10/27/2016: Test 2. Office hours are cancelled next week. Cliff Smyth will lecture next Tuesday and Thursday.
Tuesday, 11/01/2016: Cliff Smyth lectured on strong induction and returned graded tests. Solutions are in the shared folder.
Thursday, 11/03/2016: Cliff Smyth lectured on product and sum rule for counting and gave the programming assignment.
Tuesday, 11/08/2016: We covered 6.2 on the Pigeonole Principle. Read 6.3 for Thursday.
Thursday, 11/10/2016: We covered 6.3 on permutations and combinations. We learned about Python loading files and dictionaries. Read 9.1 for Tuesday.
Tuesday, 11/15/2016: We covered 9.1 on relations. Read 9.5 for Tuesday.
Thursday, 11/17/2016: We covered 9.5 on equivalence relations. The old test with solutions is in the shared folder. Test 3 is Thursday after break.
Tuesday, 11/22/2016: Introduction to turtle module in Python for optional programming assignment. Revew worksheets. Solutions are in the shared folder. No class Thursday due to Thanksgiving.
Tuesday, 11/29/2016: Review for Test 3.
Thursday, 12/01/2016: Test 3. Covers 5.1, 5.2, 6.1-6.3, 9.1-9.5 and Python.
Tuesday, 12/06/2016: Reading Day. I will hold office hours as scheduled to review for the final exam. The final exam is Saturday at 3:30 pm.