Mathematics 270 is divided into ten units, listed below.

Unit 1 Systems of Linear Equations
Unit 2 Matrix Arithmetic
Unit 3Elementary Matrices and the Matrix Inverse
Unit 4Determinants I: Cofactor Expansion and Cramer’s Rule
Unit 5Determinants II: Further Properties
Unit 6Vectors in Two and Three Dimensions
Unit 7Lines and Planes in Three Dimensions
Unit 8Introduction to Vector Spaces
Unit 9General Vector Spaces
Unit 10Linear Programming: Geometric Method

Each unit includes learning objectives, which indicate what you are expected to learn from the material; indications, which tell you the order in which to do the readings and exercises; and textual material, designed to replace the instruction you would expect to receive in a regular classroom.

Work through the units carefully. Begin by reading the objectives, and keep them in mind as you proceed through the unit. Next, do the assigned readings and exercises, in the order in which they appear in the “Indications” sections. It is important that you read each section of the Study Guide or textbook three times—first for an overview, then in more detail, and finally, with pencil in hand, working out the examples and proofs.

Exercises

Three kinds of exercises are assigned in the Study Guide: mathematical problems related to material covered in the given unit; problems assigned from the textbook; and visualization exercises. The first two types of exercises are designed to teach the conceptual and computational skills necessary for success in the course. Solutions to most of these exercises are given in the Solutions Manual or the Study Guide, but you should not look at them until you have made a concerted effort to solve each problem yourself. The visualization exercises have been included because you will find many mathematical problems or concepts much easier if you are able to visualize a concrete example.

It is important that you remember that mathematics can only be learned by doing. It is not a passive activity. Also, it is actually beneficial to be stumped at times: you are forced to think hard about a problem. When this happens, you will remember the problem and its solution more clearly.

Note: Be prepared to discuss any questions or concepts that pose problems with your tutor.

Remember that a part of your marks on the mid-term and final examinations will depend on your method. Get into the habit of showing all of your work as you go through the examples, proofs and exercises.