Math 3250 — Schedule

PLEASE REFRESH THE PAGE AT EACH VISIT!

Welcome to Math 3250: Combinatorics, this Spring 2020! Today is .

Main Page (Schedule and lecture notes)

See also UConn Calendar for Spring 2020 for important deadlines and other dates.

Lecture notes used in video lectures

Lecture Videos

Kaltura Video Playlist

YouTube Video Playlist

Please let me know which platform is more convenient (try playing on your laptop and smart phone)

Links to relevant videos

By PBS Infinite Series List of videos: Graph Theory; Video about a Catalan object Associahedra: the shapes of multiplication

News: You have until May 15 (this is after you see your grade) to put a course on pass/fail or letter grade. You have until the last day of classes to withdraw from any course and switch to Pass/Fail grading.

CURRENT: Finals Week (May 4 – 9)

Due Friday, Apr 8 at 5pm Portfolio Problems 3, template file portfolio3.tex and Figure portfolio3fig.pdf
- In the Overleaf project (I created for you), make a new folder called portfolio3, and upload the template file there. Put your homework source code there.
- Also send the PDF as an email attachment
If you want extra help with the Overleaf homework, we can do a class meeting on Thurs, 1-3pm

Past: Week 15 (Apr 27 – May 1)

Videos for this week: Plabic graphs. Both reading HW should be submitted by the end of the week.
Tue d1:
- Recommended deadline Apr 28 Reading HW 17 on plabic graphs part I (PDF), reading17.tex souce
Thurs d2:
- Recommended deadline Apr 30 Reading HW 18 on plabic graphs part II (PDF), reading18.tex souce

Past: Week 14 (Apr 20 – 24)

Videos for this week: 1.3 Trees (Tue 1.3.1–1.3.3, Thurs 1.3.4). Both reading HW should be submitted by the end of the week.
Tue d1:
- Recommended deadline Apr 21 Reading HW 15 on Trees (Overleaf link)
- 3:40pm Webex meeting to do student presentations. Email your presentation preferences before class
Thurs d2:
- Recommended deadline Apr 23 Reading HW 16 (PDF), reading16.tex source and reading16.png figure on counting trees (Cayley’s tree theorem and Matrix Tree Theorem)
- 3:40pm Webex meeting to do student presentations. Email your presentation preferences before class

Past: Week 13 (Apr 13 – 17)

No new videos, no new homework this week

Tue d1: 3:40pm Webex meeting to do exam 2 review.
Exam 2 (any day this week)
- The verbal exam should take around 30 minutes, but please schedule a 1-hour period. Pick from link of available slots or email me with other times that you are available this week.
- We will use an Overleaf project (to be shared during the exam), Webex, paper, and verbal communication.
- Usually students find verbal exams easier than written exams, But if a verbal exam makes you nervous, you can opt for a take-home exam instead. In this case, please give me a time that you would like to start the take-home exam (it would be due 8 hours later).
Exam 2:
- Topics: ordinary and exponential generating function, intro to graph theory up to Sec 1.2
- Exam 2 Study guide

Past: Week 12 (Apr 6 – 10)

Videos for this week: HHM Sec 1.1.3 Special types of graphs, 1.2 Distance of graphs
Tue d1
- Due Apr 9 Reading HW 14 (PDF), reading14.tex source on HMM Sec 1.2.2 (adjacency matrix and distance matrix)
- 3:40pm Webex meeting to do student presentations. Email your presentation preferences before class
Thurs d2
- Due Apr 7 Reading HW 13 (PDF), reading13.tex source on HHM Sec 1.1.3 (bipartite graphs and other special types of graphs) and 1.2.1 (radius and diameter)
- 3:40pm Webex meeting to do student presentations. Email your presentation preferences before class
- Discuss Exam 2 during live meeting

Past: Week 11 (March 30 – April 3)

Videos for this week: HHM Sec 1.1.1, 1.1.2 Part A-B Graph theory: The basics
Tue d1
- Due March 31 Reading HW 12 (PDF), reading12.tex source on HHM Sec 1.1.1-1.1.2
- 3:40pm Webex meeting to do student presentations. Prepare to explain two of the exercises (or at least read out loud the solutions given in the textbook)
Thurs d2
- HW before class: Prepare to explain one of these: HHM Exercise 2, Bona Exercise 3 and 10 from Reading HW 12 (PDF). Email me with your preference before class.
- No new videos to watch for Thursday
- 3:40pm Webex meeting to do student presentations.
- Deadline moved to Tue, Apr 7 Portfolio Problems 2, template file portfolio2.tex
  - In the Overleaf project (I created for you), make a new folder called portfolio2, and upload the template file there. Put your homework source code there.
  - Also send the PDF as an email attachment
  - If possible, work on this with your assigned partner (via video calls or emails) and submit one copy from both people. Ideally, you would work together instead of just dividing up the problems. If virtual collaboration is too difficult, you can each submit individually.
  - Pairing for Portolio 2 (how many ways can I assign three pairs?)
    - Austin, Steven
    - Jeffrey, Tiffany
    - Jack, Jason
    - Robin, join any pair or work on your own.

Past: Week 10 (Mar 23 – Mar 27)

Videos for this week:
- Bona Sec 8.2.1 Recurrence relations and exponential generating functions
- Bona Sec 8.2.2 Product formula for exponential generating functions
Tue d2 virtual class: Individual meeting (check email for schedule)
Thurs d2
- Due March 26 Reading HW 11 (PDF), reading11.tex source
Thurs d2 virtual class: Discuss the last exercise in Reading HW 11; Work on portfolio2 problem (Harmonic series)

Past: Week 9 (Mar 16 – 20) SPRING BREAK

Past: Week 8 (Mar 9 – 13)

Tue d1
- Due Reading HW 9 (PDF), reading9.tex source
Tue d1 in-class: Finish Sec 8.1.2.1. Catalan numbers, using triangulations.
- Practice HuskyCT Blackboard Collaborate and Google Hangout

Thurs d2
- Due Reading HW 10 (PDF), reading10.tex source
Thurs d2 in-class: Explain Sec 8.1.3. Continue Chapter 8, work in
- Scribble Together Whiteboard for watching the lecture live from your browser. We will use Webex instead. Check your email for the Webex remote address, and email me if you cannot get into the remote room.

Past: Week 7 (Mar 2 – 6)

Tue d1
- Before class, review the computation from Sec 8.1.1 Recurrence relation and ordinary generating function
- Before class, read the first two pages of Sec 8.1.2 Products of generating function
Tues d1 in-class: Lecture Example 8.8 from Sec 8.1.2 Products of generating functions; Show four types of Catalan objects (students find the 14 objects for n=4), see Sec 8.1.2.1.

Thurs d2
- Due Reading HW 8 (PDF), reading8.tex source
Thurs d2 in-class: Continue Chapter 8

Past: Week 6 (Feb 24 – Feb 28)

Tue d1 in-class: Lecture 8.1.1 Recurrence relation and ordinary generating function

Thurs d2 Exam Day

Study Guide: Chapters 1–4, Problems Week 6 (Prep for Exam 1), solution key

Past: Week 5 (Feb 17 – 21)

Tue d1
- Prior to class, attempt all problems from Problems Week 5, Source code
- If you haven’t looked at Problems Week 4, .tex yet, attempt them as well
Tue d1 in-class: lecture Sec 4.2 Multinomial Theorem and 4.3 General Binomial Theorem (review Taylor series!)

Thurs d2
- Due your writeup (presentation notes), and be ready to present
  1. Go to Google Doc
  2. Next to your name, write at least one problem from Problems Week 4 and one from Problems Week 5. It’s OK if other students pick the same problems.
  3. Optional: Show me the problems on Wed or Thurs (before class) so I can give feedback
  4. Submit your chosen problems, either handwritten or using LaTeX — show all explanation and computation, not just the answer
  5. Everyone should be prepared to present any of the problems which they submit (I will use dice)
- Bring your calendar to class. I will ask you to vote an exam date next week or the following week.
Thurs d2 in-class: Problem presentations of JJTSJA (labeled presentation 7 in grade book), and short lecture on motivation for ordinary generating function (Sec 8.1)

Past: Week 4 (Feb 10 – 14)

Tue d1
- Due Reading HW 5 (PDF), reading5.tex source
- (Vocab) QUIZ (quiz 6)
  - Q: Write down the definion of an injection. A: Let f be a function whose domain is a set X. The function f is said to be injective provided that for all a and b in X, whenever f(a) = f(b), then a = b.
  - Q: Write down the definion of a surjection. A: Let f be a function with domain X and codomain Y. We say f is surjective if for every y in Y, there exists at least one x in X with f(x) = y.
  - Q: Write down the definion of a bijection. A: A function which is both injective and surjective (using the definitions given above)
Tue d1 in-class: lecture Sec 3.3 Choice Problems, and start Sec 4.1 Binomial Theorem (and proving identities combinatorially)
Thurs d2
- Note: No office hours on Thursday, Feb 13
- Optional: Watch a connection between subsets and higher dimension Combinatorics and Higher Dimensions - Numberphile, featuring Federico Ardila
- Prior to class, attempt all problems from Problems Week 4, Source code

Thurs d2 in-class: Sec 4.1 Binomial Theorem and proving identities combinatorially

Past: Week 3 (Feb 3 – 7)

Tue d1
- Due HW 3 (Overleaf):
  - Keep source code in the Overleaf Project “Combinatorics portfolio of YourName”
  - Download PDF then email the PDF file to me
- In case of technical difficulties, use Template of HW3
- Recommended: Spend 15 minutes reading the first 10 sections of Overleaf: Learn LaTeX in 30 minutes
Tue d1 in-class: students worked on portfolio1 problems on their own, leture Sec 3.1 set and multiset permutations, students practice problems
Thurs d2
- Due Portfolio Problems 1, template file portfolio1.tex, graded by correctness
- Prior to class, get familiar with all problems from Problems Week 3, .tex source (do not submit yet)
Thurs d2 in-class: lecture Sec 3.2 Strings (words) over a finite alphabet, everyone worked on the board on Problems Week 3 in groups, sketched solutions to all problems except divisibility by 11.

Past: Week 2 (Jan 27 – Jan 31)

Tue d1:
- Due (either hand-written or typed) Reading HW 2 (PDF)
  - There is a question there which asks you request a topic to cover (but I apologize ahead of time if your topic doesn’t get covered)
  - reading2.tex source.
- Bring a laptop (I will explain Overleaf). Borrow from the library (for 4 hours at a time) or bring your own. Tablets won’t work as well.
- Before class, attempt the first four problems from Problems Week 2, .tex source.
Tues d1 in-class: Lecture Sec 2.1 weak induction, everyone worked on Week 2 problems (question 4, Fridays) in Groups
Thurs d2:
- Due (either hand-written or typed) Reading HW 4 (PDF), see source code reading4.tex
- Before class, attempt all problems from Problems Week 2
Thurs d2 in-class: Sec 2.2 strong induction, Towers of Lucas: point of view, answer questions about next week’s assignments

Past: Week 1 (Jan 21 – 25)

Tue d1: Class introduction, Lecture on Sec 1.1-1.2 Pigeon-Hole Principle
Thurs d2: Due at the end of class, either hand-written or typed Reading HW 1 PDF – if you are interested you can see the .tex source. If you are not presenting, there will be time to ask questions/ complete the problems during class on Thursday (while the presenters are setting up).
Thurs d2 in-class: Dana Ernst’s Setting the Stage 4 questions, presentations (1 Tiffany, 2 Jason, 3 Jeffrey, 4 Robin), audience (everyone)