Foundational Discrete Mathematics

Syllabus

Class Calendar

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

  • …
  • 9/5/2024 – Today we reviewed and expanded on our discussion of sets. We have now looked at the basics of set notation and building new sets form old. We then started talking about statements, sentences that are true or false, ways to think about them, and ways to combine them creating new statements from old. Here is an updated version of the Rain-Grass-Umbrella Handout from class.
  • 8/29/2024 – Today we went over the syllabus, discussed writing up mathematics, and started talking about vocabulary from chapter 1. We will finish what vocabulary we need next Thursday and start working through chapter 2.

Unit 1: Logic

Practice Exam for Unit 1 Due 9-19-2024

Assignment Due 9-26-2024

All text assignments must be written up neatly or be typed, and must be in complete sentences. Remember that 10% of your exam grade is based on the quality of your work.

  • Sec. 2.3 – 40
  • Sec. 2.4 – 23
  • Sec. 3.3 – 57 & 58
  • Sec. 3.4 – 32

Unit 2: Sequences and Summations

Practice Exam for Unit 2 Due 10-7-2024

Assignment Due 10-14-2024

All text assignments must be written up neatly or be typed, and must be in complete sentences. Remember that 10% of your exam grade is based on the quality of your work.

  • Sec. 5.1 – 87 (Compare to Algorithm 5.1.1)
  • Sec. 5.6 – 18acd (For parts (c) and (d) you answers should be focused on how \(a_n\) and \(b_n\) are defined, not numbers and formulas. That is discuss moving discs or stacks of discs.)
  • Sec. 5.7 – 54a

Unit 3: Sets, Functions, Relations

Practice Exam for Unit 3 Due 10-28-2024

Assignment Due 11-4-2024

All text assignments must be written up neatly or be typed, and must be in complete sentences. Remember that 10% of your exam grade is based on the quality of your work.

  • Sec. 6.1 – 26 (In some printings of the text there is a typo, everything should start at \(i=1\).)
  • Sec. 7.2 – 56 (Give a verbal description of what needs to happen. It will look like an if-then-else statement or a piecewise defined function.)
  • Sec. 7.3 – 20 (Use arrow diagrams to justify your answer. Extra points for a minimal example.)
  • Sec. 8.2 – 26
  • 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 and Combinatorics

Practice Exam for Unit 4 Due 11-14-2024

Assignment Due 11-21-2024

All text assignments must be written up neatly or be typed, and must be in complete sentences. Remember that 10% of your exam grade is based on the quality of your work.

  • Sec. 9.2 – 28
  • Sec. 9.4 – 8 (look at Example 9.4.3)
  • Sec. 9.5 – 17 (try looking at a smaller problem first)
  • Sec. 9.7 – 16
  • Extra Credit Sec. 9.3 – 26abcd

Unit: 5 Graph Theory

Practice Exam for Unit 5 Due 12-2-2024

Assignment Due 12-13-2024 by 3pm (before the end of finals week)

All text assignments must be written up neatly or be typed, and must be in complete sentences. Poor quality work can result in up to a 10% penalty.

  • Sec 10.1 – 28 (Answer for 2, 3, and 4 people, then try to generalize.) & 42 (You must explain your process as well as give a final answer.)
  • Sec 10.4 – 24 (Answer for graphs with 2, 3, and 4 vertices, then try to generalize.)

Final Exam Materials

Final Practice Exam Due 12/9/2024 at 2pm

The final exam for this class is at 2pm on Monday December 9th.

Extra Credit:

Typesetting Out-of-Class Work (+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/read/frptnykkgpbt
  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

Writing Math Extra Credit Assignment (+2% to final grade)

Complete this packet on Writing Up Mathematics. This assignment needs to be typed.

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.