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.

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.