Thinking and Problem Solving

Math in the Real World

Syllabus: Click here for a PDF

Course Calendar

Day 1: Tuesday, July 17

Introduction to the Course and Graphs
  • Morning: Introduction and Graph Theory
  • Afternoon: Induction and Graph Theory Proofs

Homework: Complete this worksheet. You may write your solution on your own sheet of paper, if you would like. Bring your solution to the start of the morning session tomorrow.

Day 2: Wednesday, July 18

Graph Theory
  • Morning: Spanning Trees
  • Afternoon: Traveling Salesman Problem

Homework: Complete this worksheet. You may write your solution on your own sheet of paper, if you would like. Bring your solution to the start of the morning session tomorrow.

Day 3: Thursday, July 19

Graph Theory
  • Morning: Matrices
  • Afternoon: Markov Chains

Day 4: Friday, July 20

Graph Theory
  • Morning: Matching and Bipartite Graphs
  • Afternoon: Matching and Weighted Bipartite Graphs

Homework: Complete this worksheet. You may write your solution on your own sheet of paper, if you would like. Bring your solution to the start of the morning session tomorrow.

Day 5: Monday, July 23

Combinatorics
  • Morning: Counting Methods
  • Afternoon: Binomial Coefficients and Pascal's Triangle

Day 6: Tuesday, July 24

Proability
  • Morning: Introduction to Probability
  • Afternoon: Expected Value

Day 7: Wednesday, July 25

Probability
  • Morning: Conditional Probability and Independent Events
  • Afternoon: Applications of Probability

Day 8: Thursday, July 26

Presentations and MoMath
  • Morning: Working on Presentations
  • Afternoon: Field Trip to the Museum of Mathematics

Day 9: Friday, July 27

Biology
  • Morning: Population Growth
  • Afternoon: Shapes of Nature

Day 10: Monday, July 30

Finance
  • Morning: Stocks and Investments
  • Afternoon: Loans

Day 11: Tuesday, July 31

Game Theory
  • Morning: Introduction to Game Theory
  • Afternoon: Nash Equilibria

Homework: Complete this worksheet.

Day 12: Wednesday, August 1

Cryptography and Number Theory
  • Morning: Basic Cyphers
  • Afternoon: Introduction to Number Theory

Day 13: Thursday, August 2

Number Theory and RSA
  • Morning: More Number Theory
  • Afternoon: RSA and Public Key Encryption

Day 14: Friday, August 3

Presentations
  • Morning: Presentations
  • Afternoon: Presentations

List of Applications

At the end of the course, each student will give a 10-15 minute presentation on an application of mathematics to the real world. The following is a list of potential subjects. Students should explore the list below and choose an application which the student finds interesting. Students may choose to present about an application not on this list, with approval from the instructor.

  • Alpha Go and automated game-playing
  • Map making
  • Error-correcting codes
  • Data compression
  • Special Effects
  • Epidemeology
  • Crime Investigation
  • Aerodynamics
  • Signal Processing
  • Radar and Other Object-Detection
  • Speach Processing (think: Siri, Alexa, Google)
  • Facial Recognition
  • Big Data
  • Animal Locomotion
  • String Theory and our Multidimensional Universe
  • Gerymandering
  • DNA
  • Lottery Games
  • Random Numbers in Cryptography
  • Gears and Clockwork
  • Weather Prediction
  • Partitioning
  • Matching Residents with Hospitals

Other Resources

  • An Introduction to LaTeX: This worksheet was built for a previous class. It has not been edited for this class, however the LaTeX instructions are still just as applicable.