Exam Policy:
No books or electronic devices are allowed on the midterm or exam. No collaboration is permitted at the midterm or exam.
THERE WILL BE NO MAKE-UPS FOR EXAMS.
The midterm will be in-class on Wednesday, October 20; it will be 50 minutes long.
Students with special exam-taking requirements or time conflicts should contact me by October 1.
Quiz Policy:
There will be one 25 minute quiz on Wednesday, October 13 (note this was changed from an earlier version of the syllabus).
It can be thought of as practice for the midterm. No books or electronic devices are allowed on quizzes. No collaboration is permitted on quizzes. THERE WILL BE NO MAKE-UPS FOR QUIZZES.
Homework Policy: You may consult each other and the textbook above.
List all people and sources who aided you and whom you aided, and write up the solutions independently, in your own language.
It is easy nowadays to find solutions to almost anything online.
DO NOT consult such solutions until after turning your homework.
Solutions to homeworks will be handed out in class and/or discussed in class.
Late homeworks will not be accepted.
Please visit this site frequently for new information.
Updates to the syllabus and reading assignments, homeworks, and practice exams will be posted here as the course progresses.
Syllabus
Since we are using multiple textbooks, there will be some overlap with the reading assignments. The most important/relevant sources will be listed first.
Week 1: Sep 20, Sep 22, Sep 24
Set theory, functions, and the watermelon cutting problem: read the handout
Joy of Sets, Section 1.2 and Theorem 1.3.1 of LPV (the textbook Discrete Mathematics: Elementary and Beyond).
Read the handout
Mathematical Hygiene. We will discuss some of these concepts throughout the course as needed.
Homework 1 due Sep 29
Correction: In Problem 1.9, the right hand side of the recurrence should have a factor m+1 in front, not m.
Week 2: Sep 27, Sep 29, Oct 01
Pascal's triangle, counting, bijective proofs, inclusion-exclusion: Sections 1.7-1.8, 3.5-3.6, 2.3 of LPV
Wikipedia article on inclusion-exclusion
Homework 2 due Oct 6.
Week 3: Oct 04, Oct 06, Oct 08
Inclusion-exclusion, Fibonacci numbers: Sections 6.9, 4.1-4.3 of LPV
Homework 3.
Update 10/14/21: Homework 3 is now due Monday Oct 18 since we did not cover domino tilings on Wednesday.
Week 4: Oct 13, Oct 15
Fibonacci numbers, generating functions: 1.1-1.3, 2.1-2.2 of generatingfunctionology
There will be a 25 minute quiz at the end of class on Wednesday, October 13.
About half the points will be proofs and half short answer. It will mainly cover the material on homeworks 1 and 2 and may include anything we covered in class up to but not including inclusion-exclusion.
Homework 4 due Oct 27
(no homework due October 20 because of the midterm)
Week 5: Oct 18, Oct 20, Oct 22
Generating functions continued: 1.1-1.3, 2.1-2.2 of generatingfunctionology
Midterm: Wednesday, October 20 in class.
Week 6: Oct 25, Oct 27, Oct 29
Catalan numbers, generating functions: Chapter 2 of generatingfunctionology
Homework 5 due Nov 10
Week 7: Nov 1, Nov 3, Nov 5
Introduction to graph theory: vertex degrees, trees, paths, cycles: Ch. 1-2 of West or Sections 7.1-7.2, 8.1-8.2, 13.2 of LPV
Week 8: Nov 8, Nov 10, Nov 12
Trees, Kruskal's algorithm: Ch. 2 of West
Homework 6 due Nov 17
Week 9: Nov 15, Nov 17, Nov 19
Euler's formula, Platonic solids, Graph coloring: Ch. 6.1 and 5.1 of West
Week 10: Nov 22
Coloring planar graphs: Ch. 6.3 of West
Week 11: Nov 29, Dec 01, Dec 03
Hall's matching theorem: Ch. 3 of West
Disability Resources:
Students
requesting accommodations due to a disability at Drexel University need to request a current Accommodations Verification Letter (AVL) in the
ClockWork database before accommodations can be made. These requests are received by Disability Resources (DR), who then issues the AVL to the appropriate contacts. For additional information, visit the DR website at
drexel.edu/oed/disabilityResources/overview/, or contact DR for more information by phone at 215.895.1401, or by email at disability@drexel.edu.
Outcomes:
Students must understand basic mathematical language including sets and functions, apply mathematical induction, count or enumerate objects using various combinatorial formulas, operate with discrete structures including graphs and permutations, and describe simple algorithms.
Students will be comfortable writing short mathematical proofs including proofs by induction, bijective proofs, and proofs in number theory.