Schedule

This schedule is tentative and subject to change.

Warmups are due every class day, even if they are not listed under the “Due” column.

Week 1

M Sep. 09	Welcome!
M Sep. 09	We discuss the structure of the course and the role of mathematics in modern computation.
	Learning Objectives Getting Oriented		In Class Welcome!	Due Join EdStem and Gradescope.
W Sep. 11	Mathematics and Me
W Sep. 11	We discuss our relationship to math and how we've learned what we've learned.
	Learning Objectives Getting Oriented	Prep Math Autobiography	In Class Mathematics and Me
F Sep. 13	Lab 1: Technical Writing and Truth Tables
F Sep. 13	We review truth tables for describing logical operations and begin our first lab assignment in Google Colab.
		Prep Statements and Truth Tables	In Class Lab 1: Technical Writing and Truth Tables

Week 2

M Sep. 16	More Logic: Equivalence, Conditionals, and Biconditionals
M Sep. 16	We introduce formal manipulations of logical expressions and work with the many ways to manipulate conditional statements.
		Prep More Logic: Equivalence, Conditionals, and Biconditionals	In Class Logic Practice
W Sep. 18	Introducing Set Theory
W Sep. 18	We introduce sets, set-builder notation, and operations for combining and measuring sets.
	Learning Objectives S1, S2	Prep Introducing Set Theory	In Class Practice with Sets
F Sep. 20	Lab 2: Inclusion-Exclusion
F Sep. 20	We use the inclusion-exclusion formula and its generalizations to compute the cardinality of unions of sets. Along the way, we practice writing mathematical computations and performing computational experiments.
	Learning Objectives S2	Prep Cardinality and Complements	In Class Lab 2: Inclusion-Exclusion	Due Lab 1: Technical Writing and Truth Tables

Week 3

M Sep. 23	Quantifiers and Predicate Logic
M Sep. 23	We discuss quantification of propositions over sets and how to apply logical operations to symbolic quantifiers.
	Learning Objectives L1, L2	Prep Quantifiers and Predicate Logic
W Sep. 25	Logical Deduction
W Sep. 25	We introduce logical deduction as a formal method for drawing conclusions from a set of premises.
	Learning Objectives L3	Prep Logical Deduction
F Sep. 27	Quiz 1
F Sep. 27	The first of four quizzes in which students have an opportunity to complete Learning Targets.
			Due Lab 2: Inclusion-Exclusion

Week 4

M Sep. 30	Direct Proof and the Element Method
M Sep. 30	We introduce direct proofs, our first general technique for proving statements about mathematics and algorithms. We then focus on the element method, which is used for proving that one set is a subset of another set.
	Learning Objectives PF1	Prep Direct Proof and the Element Method
W Oct. 02	Cases, Contradictions, and Counterexamples
W Oct. 02	We introduce several additional proof techniques, as well as the practice of counterexamples for disproving incorrect implications.
	Learning Objectives PF2	Prep Cases, Contradictions, and Counterexamples
F Oct. 04	Lab 3: Proof Practice
F Oct. 04	We practice proving mathematical statements using a variety of techniques.
	Learning Objectives PF1, PF2	Prep Modular Congruence and Proofs as Writing	In Class Lab 3: Proof Practice

Week 5

M Oct. 07	Relations
M Oct. 07	We introduce relations, with a special focus on equivalence relations on sets.
	Learning Objectives FR1	Prep Relations and Equivalence Relations
W Oct. 09	Induction
W Oct. 09	We introduce mathematical induction, a powerful proof technique for demonstrating that a claim is true for infinitely many cases.
	Learning Objectives PF3, PF4, PF5	Prep Introduction to Induction
F Oct. 11	No Class: Midterm Recess
F Oct. 11
			Due Lab 3: Proof Practice

Week 6

M Oct. 14	More Induction
M Oct. 14	We broaden our usage of induction to prove inequalities and write inductive proofs for the correctness of functions.
	Learning Objectives PF3, PF4, PF5, PF6	Prep More Induction
W Oct. 16	Strong Induction
W Oct. 16	We introduce strong induction as an additional tool for proving mathematical theorems.
	Learning Objectives PF7	Prep Strong Induction
F Oct. 18	Quiz 2
F Oct. 18	The second of four quizzes in which students have an opportunity to complete Learning Targets.
			Due Lab 3: Proof Practice

Week 7

M Oct. 21	Counting
M Oct. 21	We use the principles of addition, multiplication, and inclusion-exclusion to solve counting problems.
	Learning Objectives C1	Prep Counting	In Class Counting at Noonies
W Oct. 23	Permutations and Combinations
W Oct. 23	We use permutations and combinations to count possibilities in situations involving rearrangement and subset-selection.
	Learning Objectives C2	Prep Permutations and Combinations
F Oct. 25	Lab 4: Counting Lattice Paths
F Oct. 25	We use binomial coefficients and Python programming to efficiently compute the number of paths through grids.
	Learning Objectives C1, C2	Prep Counting Lattice Paths	In Class Lab 4: Counting Lattice Paths

Week 8

M Oct. 28	Recurrence Relations
M Oct. 28	We introduce recurrence relations, the guess-and-check method for solving them, and proving solutions using induction. We also wave a quick hello at the Fibonacci numbers, a famous sequence of integers defined using recurrence relations.
	Learning Objectives R1	Prep Recursion and Recurrence Relations	In Class Combinatorics of Fibonacci Numbers
W Oct. 30	Recursion and Recurrence Relations
W Oct. 30	We practice writing recurrence relations to describe quantities of interest and develop further techniques to solve them.
	Learning Objectives R1	Prep Recursion and Recurrence Relations in Algorithms	In Class Tower of Hanoi
F Nov. 01	Lab 5: Analyzing Gradient Descent
F Nov. 01	We use recurrence relations to analyze the runtime of an algorithm for minimizing a function.
	Learning Objectives R1	Prep None	In Class Lab 5: Analyzing Gradient Descent	Due Lab 4: Counting Lattice Paths

Week 9

M Nov. 04	Asymptotics and Big-Oh
M Nov. 04	We formally define big-oh notation and prove asymptotic descriptions of various functions.
	Learning Objectives R2	Prep Asymptotics and Big-Oh Notation
W Nov. 06	No Class
W Nov. 06	We spend our time emotionally recovering from the US election, with optional Student Hours for students who want to review prior to Quiz 3.

F Nov. 08	Graphs
F Nov. 08	We introduce graphs as models of data structures and connected systems.
	Learning Objectives G1	Prep Introducing Graphs

Week 10

M Nov. 11	Quiz 3
M Nov. 11	The third of four quizzes in which students have an opportunity to complete Learning Targets.
				Due Lab 5: Gradient Descent
W Nov. 13	Trees
W Nov. 13	We continue our discussion of graphs with a focus on trees.
	Learning Objectives G1	Prep Trees
F Nov. 15	Lab 6: Triangle-Counting
F Nov. 15	We study the adjacency matrix of a graph and use it to count the number of triangles in real and synthetic graph data sets.
	Learning Objectives G1	Prep The Adjacency Matrix of a Graph	In Class Lab 6: Introduction to Network Science

Week 11

M Nov. 18	Introducing Discrete Probability
M Nov. 18	We introduce the fundamental principles of discrete probability.
	Learning Objectives PR1	Prep Introducing Discrete Probability	In Class Practice with Outcomes and Events
W Nov. 20	Conditional Probability and Bayes' Rule
W Nov. 20	We introduce methods for calculating conditional probabilities from other probabilities, including the idea of learning from data expressed by Bayes' Rule.
	Learning Objectives PR1, PR2	Prep Conditional Probability and Bayes' Rule	In Class Bayes' Rule and DNA Testing
F Nov. 22	Lab 7: TBD
F Nov. 22
	Learning Objectives Probability			Due Lab 6: TBD

Week 12

M Nov. 25	No Class: Thanksgiving Break
M Nov. 25

W Nov. 27	No Class: Thanksgiving Break
W Nov. 27

F Nov. 29	No Class: Thanksgiving Break
F Nov. 29

Week 13

M Dec. 02	Random Variables and Expectation
M Dec. 02	We introduce random variables as models of randomized quantities, and expectations as models of averages of these quantities.
	Learning Objectives PR2	Prep Random Variables and Expectation
W Dec. 04	More on Random Variables and Expectation
W Dec. 04	We introduce several properties of expectation, and introduce the variance of random variables.
	Learning Objectives PR3	Prep More on Random Variables and Expectation
F Dec. 06	Example: The Erdős-Rényi Random Graph
F Dec. 06
	Learning Objectives PR3	Prep Computing Properties of the Erdős-Rényi Random Graph

Week 14

M Dec. 09	Quiz 4
M Dec. 09
		Due Lab 7: TBD

Final Exam

Our final exam will be another quiz covering all twenty Learning Targets. So, it’s just like Quiz 4, except you’ll have 3 hours instead of 50 minutes.