MATH 100 - The Art of Mathematical Thinking: An Introduction to the Beauty and Power of Mathematical Ideas

FDR: FM
Credits: 3

Spring 2020, MATH 100-01: The Art of Mathematical Thinking: Solving Puzzles and Games Using Mathematics (3). Any high school mathematics class is sufficient preparation for this material. Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this course, we focus on mathematical reasoning to analyze various puzzles and games, which then leads to figuring out how to increase our chances of winning. The springboard for our discussion comes from the answers to the following questions: 1) Is there a good way to predict the winner of a game before the game ends? 2) Is there a strategy that will improve a player’s chance of winning a game? 3) Is the game fair? The answers depend on what we mean by good and fair. We start by carefully and precisely formulating environments in which we can discuss approaches to solving puzzles and playing games. Then, we contemplate criteria that capture the notions of goodness and fairness within these environments. Along the way, students learn the importance of precise definitions and consistent rules of logic in mathematical reasoning. (FM) Finch-Smith.

Winter 2020, MATH 100-01: The Art of Mathematical Thinking: Introduction to Codes (3). Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this section, students explore the use of and questions about the numbers and codes which are everywhere. You might have a driver’s license number, a Social Security Number, a student identification number, a telephone number, credit-card numbers–the list goes on and on. If you’re filing out a form and you’re asked for an identification number, will anyone be able to tell right away if you’ve made up a number? If someone is typing your information into a computer, is there a way to make sure they haven’t made any errors? How are credit-card numbers kept safe when we make online purchases? We discuss types of errors, algorithms for checking for errors, and some methods for encrypting information to keep it secure. The only skills needed to enter this course are arithmetic and intellectual curiosity. Students learn how to analyze algorithms and develop problem-solving skills throughout the course. (FM) Finch-Smith.

Fall 2019, MATH 100-01: The Art of Mathematical Thinking: The Mathematics of Politics (3). Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this course, we focus on mathematical reasoning about politics. What makes this course mathematical is not numbers or formulas but rather reasoning. Students must think about what is possible and what is impossible. Is there a good way to determine winners of elections? Is there a good way to apportion congressional seats? Is there a good way to make decisions in situations of conflict and uncertainty? We begin by carefully and precisely formulating environments in which we can discuss approaches to elections, apportionment, and rational decision-making. We contemplate criteria that capture the notions of goodness within these environments, and see importance of precise definitions and consistent rules of logic in mathematical reasoning. Throughout the course, we pay attention to the way that technical words are defined so that the precise technical meaning is not confused with the ordinary meaning that the word carries in natural language. (FM) Finch-Smith.
 
Fall 2019, MATH 100-02: The Art of Mathematical Thinking: The Mathematics of Politics (3). Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this course, we focus on mathematical reasoning about politics. What makes this course mathematical is not numbers or formulas but rather reasoning. Students must think about what is possible and what is impossible. Is there a good way to determine winners of elections? Is there a good way to apportion congressional seats? Is there a good way to make decisions in situations of conflict and uncertainty? We begin by carefully and precisely formulating environments in which we can discuss approaches to elections, apportionment, and rational decision-making. We contemplate criteria that capture the notions of goodness within these environments, and see importance of precise definitions and consistent rules of logic in mathematical reasoning. Throughout the course, we pay attention to the way that technical words are defined so that the precise technical meaning is not confused with the ordinary meaning that the word carries in natural language. (FM) Finch-Smith.

  Finch-Smith.