MATH/COMP 61: Sections 03, 04
Discrete Mathematics
Spring 2020


Instructor: Karen Edwards
Office: Halligan 221
Email: kedwardsREMOVE@cs.tufts.edu (delete the word REMOVE)
Office Hours: Please see post on Piazza for times and link

Lectures:
Section 03 is C block (TWF 9:30-10:20), Eaton 206
Section 04 is D block (M 9:30-10:20, TR 10:30-11:20), Anderson 206

Announcements:
Announcements for this course will be sent to your email via Piazza. Please register as soon as possible. The access code will be given in class.

Course Materials:
All course materials for this class will be posted under "Resources" in Piazza. We will not use Canvas for this class.

Grad TAs: (all email addresses are @tufts.edu)

Undergrad TAs: (all email addresses are @tufts.edu unless otherwise noted)

Office hours: All office hours (including cancellations) will be posted in Piazza.

Description: This class covers foundations of discrete mathematics and introduction to proofs. Topics include Propositional Logic, Sets, Counting, Relations (inlcuding Equivalence Relations and Functions), Methods of Proof, Modular Arithmetic, RSA Cryptography and Graph Theory.

Textbook: We are using Mathematics: A Discrete Introduction (2nd edition OR 3rd edition) by Edward Scheinerman. It is available in many places, in multiple formats (new, used, rental, digital).

Schedule:
D block (M 9:30, TR 10:30) C block (TWF 9:30) Hwk # Sections Topic(s)
Jan 16 Jan 15 1 1–2 Questionnaire/Intros/Syllabus; Thinking Logically
Jan 21 Jan 17 1 3–4 The Integer Sandbox; Theorems
Jan 22 Jan 21 2 5–6 Proofs; Counterexamples
Jan 23 Jan 24 2 7 Boolean Algebra; Syllogisms
Jan 27 Jan 28 3 8–9 Lists; Factorial
Jan 28 Jan 29 3 10–11 Intro to Sets; Quantifiers
Jan 30 Jan 31 3 8–11 ((worksheet))
Feb 3 Feb 4 4 12 Set Operations & Proofs
Feb 4 Feb 5 - 1–12 ((review))
Feb 6 Feb 7 - 1–12 Exam 1

D block (M 9:30, TR 10:30) C block (TWF 9:30) Hwk # Sections Topic(s)
Feb 10 Feb 11 5 13–14 Combinatorial Proofs; Relations
Feb 11 Feb 12 5 15 Equivalence Relations
Feb 13 Feb 14 5 13–15 ((worksheet))
Feb 18 Feb 18 6 16–17 Partitions; Binomial Coefficients
Feb 19 Feb 20 6 17 cont. Binomial Coefficients; worksheet
(none) Feb 21 6 16-17 ((Optional worksheet/homework day))
Feb 24 Feb 25 7 20 Proof by Contradiction and Contrapositive
Feb 25 Feb 26 7 22 Induction
Feb 27 Feb 28 7 20, 22 ((worksheet))
Mar 2 Mar 3 8 22 cont. Strong Induction
Mar 3 Mar 4 8 24–25 Functions; Pigeonhole Principle
Mar 5 Mar 6 8 22, 24, 25 ((worksheet))
Mar 9 Mar 10 - 13–17, 20, 22, 24–25 ((review))
Mar 10 Mar 11 - 13–17, 20, 22, 24–25 Exam 2
Mar 12 Mar 13 9 25, 29 ((Optional bonus material: Big-O, Cantor's Thm))

D block (M 9:30, TR 10:30)
MonTue: Live lecture, recorded
C block (TWF 9:30)
TueWed: Live lecture, not recorded
Hwk # Sections Topic(s)
(none, C-block recorded) Mar 25 10 35, 36 Mod operation, Euclid's Algorithm
Mar 26 Mar 27 10 35, 36 ((worksheet))
Mar 30 Mar 31 11 37 Modular arithmetic
Mar 31 Apr 1 11 43 Fermat's Little Thm, Euler's Thm
Apr 2 Apr 3 11 37, 43 ((worksheet))
Apr 6 Apr 7 12 44, 46 RSA Cryptography
Apr 7 Apr 8 12 47, 48 Graphs: Intro & Subgraphs
Apr 9 Apr 10 12 44, 46, 47, 48 ((worksheet))
Apr 13 Apr 14 13 49, 50 Graphs: Connectedness & Trees
Apr 14 Apr 15 13 51, 52, 53 ((Optional bonus material: Eulerian Graphs, Coloring, Planar Graphs))
Apr 14 Apr 15 13 49,50 ((worksheet))
Apr 21 Apr 21 14 35-37, 43, 44, 46-50 ((review))
Apr 22 Apr 23 14 35-37, 43, 44, 46-50 Exam 3
Apr 27 Apr 24 14 ((all)) ((Review for final))

Grading: Your grade is based on 3 exams plus a final, plus your hw as follows. 80% of your grade is based on e1+e2+e3+f+f, except you get to drop the lowest of the 5 scores (final is 2 scores). 20% is based on homework.

Homework: HW assignments are posted on Piazza and will be submitted via Gradescope. Instructions for submitting homework will be posted on Piazza. Homeworks are usually due Sundays at 11:59pm.

Late homework: You are allowed four "tokens" to be used at your discretion for a 24-hour automatic extension on the homework. Other than this, late homework will be counted as 0. You are responsible for keeping track of whether you have used the tokens or not; computations are simply based on the timestamp from Gradescope on your submission. Gradescope will be set to allow homework to be submitted up to 48 hours late; if you submit it 24-48 hours after the deadline you will use 2 tokens.

HW collaboration policy: You are welcome to talk to the Instructor, TAs or other students about HW problems, but if so please follow the "sandwich" rule:

You should not be looking up hw solutions on the Internet. If you have substantially collaborated with other students on a problem, please acknowledge this at the top of that problem, i.e. "I worked with Alex and Robin". The write up still needs to be your own. In general, you should assume that problems require justification---no credit for correct answers with no justification.

Typesetting homeworks using LaTeX (optional but recommended): In order to run LaTeX you will need to install a free LaTeX distribution. You can get help at SOS Tech Help! (see above). Alternatively, you can use the lab machines, remote login (ssh & sftp) (non EECS majors can get an account @ EECS systems office), or online LaTeX editors such as Overleaf.

(thanks to COMP 160 page for the above info.)

Exams:

Final Exam: We will use the standard Tufts final exam blocks.

**The actual exam will be given for a slightly longer period (starting 15 min early, ending 15 min late) to account for technical overhead since it will be administered online.

Missing homeworks/exams:If you have a serious reason for not submitting homework or not taking an exam, you should notify your Dean and/or Health Services, and of course you may copy us as well. Decisions about missed homeworks/exams will be made in consultation with your Dean. Otherwise, exams must be taken at the scheduled times. Check the exam schedule before making travel arrangements.