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. 11	Welcome!
M Sep. 11	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. 13	Mathematics and Me
W Sep. 13	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. 15	Lab 1: Technical Writing and Truth Tables
F Sep. 15	We review truth tables for describing logical operations and begin our first lab assignment in Google Colab.
	Learning Objectives Getting Oriented	Prep Statements and Truth Tables	In Class Lab 1: Technical Writing and Truth Tables

Week 2

M Sep. 18	Working with Symbolic Logic
M Sep. 18	We introduce formal manipulations of logical expressions and work with the many ways to manipulate conditional statements.
	Learning Objectives Sets and Logic	Prep Conditionals and Friends	In Class Conditionals and Friends
W Sep. 20	Sets and Set Operations
W Sep. 20	We introduce sets, set-builder notation, and operations for combining and measuring sets.
	Learning Objectives Sets and Logic	Prep Sets	In Class Sets
F Sep. 22	Lab 2: Inclusion-Exclusion
F Sep. 22	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 Sets and Logic	Prep More on Sets	In Class Lab 2: Inclusion-Exclusion	Due Lab 1: Technical Writing and Truth Tables

Week 3

M Sep. 25	Quantifiers and Predicate Logic
M Sep. 25	We discuss quantification of propositions over sets and how to apply logical operations to symbolic quantifiers.
	Learning Objectives Sets and Logic	Prep Quantifiers and Predicate Logic	In Class Quantifiers and Predicate Logic
W Sep. 27	Further Topics: Logic and Sets
W Sep. 27	We introduce logical deduction and review topics from the course so far.
	Learning Objectives Sets and Logic Proof	Prep More on Quantifiers and Logic	In Class TBD
F Sep. 29	Quiz 1
F Sep. 29	The first of four quizzes in which students have an opportunity to complete Learning Targets. This quiz includes targets LS1, LS2, and LS3.
				Due Lab 2: Inclusion-Exclusion

Week 4

M Oct. 02	Direct Proofs
M Oct. 02	We introduce direct proofs, our first general technique for proving statements about mathematics and algorithms.
	Learning Objectives Proof techniques	Prep Direct Proofs	In Class TBD
W Oct. 04	Cases, Contradictions, and Counterexamples
W Oct. 04	We introduce several additional proof techniques, as well as the practice of counterexamples for disproving incorrect implications.
	Learning Objectives Proof techniques	Prep Cases, Contradictions, and Counterexamples
F Oct. 06	Lab 3: Proof Practice
F Oct. 06	We practice proving mathematical statements using a variety of techniques.
	Learning Objectives Proof techniques	Prep Proof Style	In Class Lab 3: Proof Practice

Week 5

M Oct. 09	Induction
M Oct. 09	We introduce mathematical induction, a powerful proof technique for demonstrating that a claim is true for infinitely many cases.
	Learning Objectives Proof techniques	Prep Introduction to Induction
W Oct. 11	More Induction
W Oct. 11	We broaden our usage of induction to use strong induction and to write inductive proofs for the correctness of functions.
	Learning Objectives Proof techniques	Prep More Induction
F Oct. 13	No Class: Midterm Recess
F Oct. 13
			Due Lab 3: Proof Practice

Week 6

M Oct. 16	Relations
M Oct. 16	We introduce relations, with a special focus on equivalence relations on sets.
	Learning Objectives Relations and functions	Prep Relations
W Oct. 18	Functions
W Oct. 18	We introduce functions, with a focus on recursive definitions of functions.
	Learning Objectives Relations and functions	Prep Functions
F Oct. 20	Quiz 2
F Oct. 20	The second of four quizzes in which students have an opportunity to complete Learning Targets. This quiz includes targets LS1, LS2, LS3, PF1, PF2, and FR1.
			Due Lab 3: Proof Practice

Week 7

M Oct. 23	Counting
M Oct. 23	We use the principles of addition, multiplication, and inclusion-exclusion to solve counting problems.
	Learning Objectives Counting	Prep Counting	In Class Counting Activity
W Oct. 25	Permutations and Combinations
W Oct. 25	We use permutations and combinations to count possibilities in situations involving rearrangement and subset-selection.
	Learning Objectives Counting	Prep Permutations and Combinations
F Oct. 27	Lab 4: Counting Lattice Paths
F Oct. 27	We use binomial coefficients and Python programming to efficiently compute the number of paths through grids.
	Learning Objectives Counting	Prep Counting Lattice Paths	In Class Lab 4: Counting Lattice Paths

Week 8

M Oct. 30	Recursion and Recurrence Relations
M Oct. 30	We introduce recurrence relations and simple methods for solving them.
	Learning Objectives Recurrence Relations	Prep Recursion and Recurrence Relations	In Class Tower of Hanoi
W Nov. 01	Recursion and Recurrence Relations
W Nov. 01	We practice writing recurrence relations to describe quantities of interest and develop further techniques to solve them.
		Prep More Recursion and Recurrence Relations	In Class Parking Spaces
F Nov. 03	Lab 5: Analyzing Gradient Descent
F Nov. 03	We use recurrence relations to analyze the runtime of an algorithm for minimizing a function.
		Prep Numerical Algorithms	In Class Lab 5: Analyzing Gradient Descent	Due Lab 4: Counting Lattice Paths

Week 9

M Nov. 06	Asymptotics and Big-Oh
M Nov. 06	We formally define big-oh notation and prove asymptotic descriptions of various functions.
	Learning Objectives Asymptotics	Prep Asymptotics and Big-Oh Notation
W Nov. 08	Analyzing Algorithms: The Tree Method
W Nov. 08	We use the tree method and other methods to estimate asymptotic runtimes of common algorithms.
	Learning Objectives Asymptotics	Prep Analyzing Algorithms
F Nov. 10	Graphs
F Nov. 10	We introduce graphs as models of data structures and connected systems.
	Learning Objectives Graph Theory	Prep Graphs and Graph Theory	Due Lab 5: Gradient Descent

Week 10

M Nov. 13	Quiz 3
M Nov. 13	The third of four quizzes in which students have an opportunity to complete Learning Targets. This quiz includes targets LS1, LS2, LS3, PF1, PF2, FR1, C1, C2, and R1.

W Nov. 15	Graphs
W Nov. 15	We continue our discussion of graphs with a focus on trees.
	Learning Objectives Graph Theory	Prep More Graph Theory
F Nov. 17	Lab 6: Triangle-Counting
F Nov. 17	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 Graph Theory	Prep Network Science	In Class Lab 6: Introduction to Network Science

Week 11

M Nov. 27	Introducing Discrete Probability
M Nov. 27	We introduce discrete probability through a discussion of a famous problem.
	Learning Objectives Probability	Prep Introducing Discrete Probability
W Nov. 29	Sample Spaces and Conditional Probability
W Nov. 29	We introduce formal discrete probability theory via sample spaces. We also introduce conditional probability.
	Learning Objectives Probability	Prep Sample Spaces, Conditional Probability	In Class Sample Spaces, Conditional Probability
F Dec. 01	Lab 7: TBD
F Dec. 01
	Learning Objectives Probability			Due Lab 6: TBD

Week 12

M Dec. 04	Bayes' Theorem
M Dec. 04	We continue our discussion of conditional probability and introduce Bayes' Theorem.
	Learning Objectives Probability	Prep Conditional Probability and Bayes' Theorem	In Class Bayes' Rule and DNA Testing
W Dec. 06	Random Variables and Expectation
W Dec. 06	We define random variables and compute the expected value of simple random variables.
	Learning Objectives Probability	Prep Random variables and expectation	In Class TBD
F Dec. 08	Quiz 4
F Dec. 08
				Due Lab 7: TBD

Week 13

M Dec. 11	Flex, Review
M Dec. 11

Final Exam

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