# 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! 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 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 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 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 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 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 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 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 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 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 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 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 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 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 Due Lab 3: Proof Practice

## Week 6

 M Oct. 16 Relations We introduce relations, with a special focus on equivalence relations on sets. Learning Objectives Relations and functions Prep Relations W Oct. 18 Functions We introduce functions, with a focus on recursive definitions of functions. Learning Objectives Relations and functions Prep Functions F Oct. 20 Quiz 2 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 Learning Objectives Probability Due Lab 6: TBD

## Week 12

 M Dec. 04 Bayes' Theorem 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 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 Due Lab 7: TBD

## Week 13

 M Dec. 11 Flex, Review

## 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.