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.