Syllabus

Full Notes Packet

If you find errors in the notes for MAT 141 Foundational Discrete Mathematics, then please fill out the following form: https://forms.office.com/r/y8vLJwZvSS. Each error submitted can earn you an extra 0.5% on your grade up to +3% extra total.
If you are comfortable DOING SO, you can instead create an “issue” on the GitHub repository where the code for the notes is stored: https://github.com/cfroccajr/MAT-141-Foundational-Discrete-Math-Notes/issues

Class Calendar

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

…
2/3/2026: We covered the material on conditionals though the discussion on Modus Ponens, Modus Tollens, the Converse Error, and the Inverse Error. This included a discussion of when a implication, \(P\rightarrow Q\), is true or false and of the converse, inverse, contrapositive, and negation of the implication. If you have not already brought in a three ring binder to pick up a notes packet then you need to do so as soon as possible so you can better follow along in class.
1/30/2026: We went over the first few pages of the notes packet; up to the page with lists of logical rules. If you have not already done so you need to bring in a three ring binder to hold the notes.
1/27/2026: Today we covered more notation including more practice with set builder notation, interval notation, Cartesian Products of sets (\(A\times B\)), functions, relations, universal quantifiers (\(\forall\)), and existential quantifiers (\(\exists\)).
1/23/2026: Today we went over the syllabus, discussed set roster and builder notation, and briefly discussed ands (\(\wedge\)), ors (\(\vee\)), intersections (\(\cap\)), and unions (\(\cup\)). We also reviewed the sets \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\), \(\mathbb{R}\), and \(\mathbb{C}\).

Unit 1: Logic

Writing Up Mathematics Assignment Due 2/3

Practice Exam for Unit 1 Due 2/17

Unit 2: Sequences and Summations

Practice Exam for Unit 2 Due 3/10

Unit 3: Sets, Functions, Relations

Practice Exam for Unit 3 Due 4/10

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 5/8

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

Create an account at Overleaf.com using your WCSU email account
Watch the introductory video here VIDEO LINK, the document created in the video is here: https://www.overleaf.com/read/khbktbvvvkjd
Follow this link to see samples of typed up exercises: https://www.overleaf.com/read/frptnykkgpbt
Follow this link to make a copy of a blank template: https://www.overleaf.com/read/hwdhcvmntrvs
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:

Complete this Reflection on Quantifiers for upto +2% on your final grade.
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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.

Foundational Discrete Mathematics