Foundational Discrete Mathematics

Syllabus

Full Notes Packet

Class Calendar

There is a proposed calendar on the syllabus, but here I will record what we actually get through in each class.

  • …
  • 9/16/2026: We discussed the first few examples of sequences. We will pick up there on Friday. Remember that you must turn in your practice exam at the start of class on Friday, if you are typing it make sure to print it out. Late practice exams will get at most a 75%. We will spend 15-20 minutes answering questions about the practice exam before continuing with the new material.
  • 9/14/2026: We finished off the last of the notes on quantifiers and predicates. You now have all you need to complete the practice exam for unit 1 which is due Friday. The exam is next Monday as it says on the syllabus.
  • 9/11/2026: We looked at additional examples of predicates and quantified statements. We will finish off chapter 3 on schedule on Monday and perhaps start a little of the next unit.
  • 9/9/2026: We did another example of combining logical arguments to create larger arguments and then we introduced predicates. We discussed different ways we can “assign” values to variables in predicates, the effect of quantifiers, and how to negate quantifiers.
  • 9/4/2026: We discussed valid argument forms, critical rows, and how to combine our basic valid arguments to make longer arguments. Please try and complete practice problem 1.15 (p.18) for Wednesday so that we can go over it quickly and start on the next section. If you didn’t turn in your work today, then you need to get it to me by Wednesday if you don’t want it counted late, and you must adhere to the guidelines from the syllabus that we discussed in class.
  • 9/2/2026: Today we discussed implications, converses, inverses, contrapositives, and negations. We also looked at wheat we mean when we say something is necessary versus sufficient (it is sufficient to be a multiple of 6 in order to be a multiple of 3, it is necessary to be a multiple of 3 in order to be a multiple of 6) Me also touched on some logical argument forms, we will pick up there next time.
  • 8/31/2026: Today we started in the printed notes packet. We covered section 1.1 and 1.2 in the notes, these correspond to the start of Chapter 2 in the text. If you didn’t bring your binder today, bring it Wednesday so that you can get the notes packet. Also, recall that the Writing Up Mathematics Assignment is due on Friday.

Unit 1: Logic

Writing Up Mathematics Assignment Due 9/4

Practice Exam for Unit 1 Due 9/18

Unit 2: Sequences and Summations

Practice Exam for Unit 2 Due 10/9

Unit 3: Sets, Functions, Relations

Practice Exam for Unit 3 Due 10/30

Extra Credit Exercise: The code below will build the equivalence classes from #26 in sec. 8.2. Explain how the code works both practically and based on the definition of the relation in 26.

# Written in Python
# Empty collection of equivalence classes
EC={}
# Build equivalence classes
for i in range(3):
    for j in range(3):
        for k in range(3):
            for l in range(3):
                # New element
                temp_lst=[i,j,k,l]
                # Assign to equivalence class based on sum
                EC[sum(temp_lst)]=EC.get(sum(temp_lst),[])+[temp_lst]
# Display equivalence classes
for key in EC: print(key,":\t",EC[key])

Unit 4: Counting, Combinatorics, and Graphs

Practice Exam for Unit 4 Due 12/4

Extra Credit:

Typesetting Out-of-Class Work in \(\LaTeX\) (+5% on each typed up piece of work)

If you are doing this extra credit here is a quick reference sheet with symbols and such: Quick Reference

  1. Create an account at Overleaf.com using your WCSU email account
  2. Watch the introductory video here VIDEO LINK, the document created in the video is here: https://www.overleaf.com/read/khbktbvvvkjd
  3. Follow this link to see samples of typed up exercises: https://www.overleaf.com/latex/templates/homework-template-with-samples/zmmdzbkzvtzk
  4. Follow this link to make a copy of a blank template: https://www.overleaf.com/read/hwdhcvmntrvs
  5. Submit work by downloading a copy of the PDF you generate and printing it.

If you are having problems typing up a document and would like feedback you can share a link to it by following the directions here: https://www.overleaf.com/learn/how-to/Sharing_a_project; send me the link to view but not edit. You can see a full playlist of video lessons here: Technical Typesetting with \(LaTeX\) Playlist

Additional Extra Credit:

Links and Handouts

Vocabulary

\(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\), \(\mathbb{R}\), rational number, irrational number, set notation, set roster notation, modus ponens, modus tollens, De Morgan’s Law, negation, distribution, commutative law, associative law, \(\forall\), \(\exists\), converse, inverse, contrapositive, conjunction, disjunction,  set, subset, Cartesian product, relation, function, sequences, series, summation, summation notation \[\sum_{i=0}^n a_i=a_0+a_1+\cdots+a_n,\] product notation \[\prod_{i=0}^n a_i=a_0\times a_1\times \cdots\times a_n,\] geometric sum \[\sum_{i=0}^n a\, r^i=a+ar+ar^2+\cdots+ar^n=a\, \frac{(r^{n+1}-1)}{r-1},\] union, intersection, set difference, set complement, power set – \(\mathscr{P}(x)\), reflexive, symmetric, transitive, anti-symmetric, function, one-to-one, onto, inverses, composition, addition principle, multiplication principle, possibilities tree, combinations, factorial, permutations, binomial coefficients, multinomial coefficients, graph, walk, circuit, Euler circuit, path, tree, trail, binary tree, Hamilton circuit, closed walk, … etc.