MATH 121: Mathematical Ideas

MATH 121 is Knox College’s introduction to mathematics course. Ultimately, the three over-arching goals of the course are to have you appreciate applications of mathematics, “think mathematically,” and become a better student.

The first goal means that this course exposes you to several aspects of mathematics. These aspects should show you what mathematics is capable of. They give you a glimpse into the world of mathematics… into another way of seeing the world around you. Perceiving the world from different angles allows one to appreciate reality in a fuller sense… in a deeper way.

The second goal of this course hopes that you better understand the following three topics:

the purpose of mathematics;
performing mathematical operations; and
modeling the world using mathematics.

The third goal means that you know how to prepare for each class period, to study for each examination, and to immerse yourself in the learning environment that is college. It also means that you are familiar with the syllabus (link to syllabus) To that end, I provide the slide decks for each class period before the class is held; the calendar for the course; and separate webpages for each of the six modules of the course.

To these ends, I designed all readings, activities, and homework assignments to support these three fundamental goals. Please take advantage of them. The structure of this course will help you master the material. It will also help you become more aware of the world around you, able to see patterns, and take advantage of your insight.

What is Studied

Here are the learning modules for the course. Click on any to experience the module and better understand mathematics.

LM1: Critical Thinking and Problem Solving. The first chapter deals with how to reason through a problem. Make no mistake about it… unless you have seen a problem type before, there are few general rules for solving a problem. This chapter provides several techniques.

LM2: Set Theory. The second chapter covers set theory. There are many reasons to understand sets. One is that it forces us to think about what is possible. Another is that it ties in to logic quite closely. Finally, it also leads us to discrete probability.

LM5: The Mathematics of Growth. The first chapter provided some techniques for solving problems. The next two chapters showed that two seemingly disparate areas of mathematics follow the same rules. This chapter looks at modeling the world using simple functions. While the chapter assignment tests your skills in linear and quadratic functions, it really checks that you are able to abstract.

LM10: Probability. This chapter returns to the abstracted rules of Chapter 2. Here, we apply these rules to the question of probability. Here, we learn the basic terms and how to calculate important quantities using mathematics. Note that we are applying earlier mathematics to another applications.

This is college. Success is yours if you are willing to work for it. In most ways, college is like life. Hard, efficient work leads to success. It is all up to you.

MATH 121: Mathematical Ideas

Course Introduction

What is Studied