Problem Solving and Reasoning

The 2015 movie "The Martian" starring Matt Damon was a sci-fi movie which tells the story about a man who was left behind by his crew in Mars after they thought he died in an intense dust storm in the Red Planet.

The movie features tons of problems ranging from survival in the desolate planet to retrieval back to Earth which they all solved one after another. The movie is a beautiful example of excellent problem solving skills applied to life-saving situations.

Problem: food to survive months in the Red Planet

Solution: grow potatoes using Martian soil, his human wastes, chemical reaction to produce water, and his botany skills

Problem: communicate with the Earth

Solution: find an old rover in Mars and use it to send and receive signal to and from Earth

Problem: retrieve him back to Earth

Solution: have his crew (who were already on their way back to Earth) return to Mars to fetch him

After you graduate, and when you land a job, one of the principal skills that would impress your employer is your ability to solve problems, especially if you can do this independently and with little supervision. Some of those problems you may have already learned from school. However, a VAST majority of them can be categorized as "they-never-taught-us-at-school." So the goal of this chapter is not to solve specific problems but to learn HOW to solve generic problems. This chapter is not about the solution to a problem but about how to get to the solution. 

Intended Learning Outcomes

• Use different types of reasoning to justify statements made about mathematics and mathematical concepts

• Write clear and logical proofs

• Solve problems involving patterns and recreational problems following Polya's four steps

• Organize one's methods and approaches for proving and solving problems