Mathematics 209: Finite Mathematics

Study Guide

Introduction

In Mathematics it pays to be persistent: people who succeed in mathematics are those who do not give up after the first attempt at solving a problem, but keep trying and asking themselves, “What else can I try?”

This course in finite mathematics covers several areas of mathematics with applications in economics, business, social sciences and life sciences. The first two units review the basic concepts needed in this course. Unit 3 is dedicated to the applications of the exponential and logarithmic functions in economics. The central mathematical concepts in this course are those of matrices and matrix operations; they are covered in Unit 4. The applications of matrices are covered in Units 5 to 8.

Your textbook is a custom publication, made exclusively for this course, and derived from

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Study your textbook following the instructions give in the “Indications” sections of this Study Guide. We recommend that you do the “Explore & Discuss” questions to get a deeper understanding of the concepts presented, and complete all the matched exercises by the time you finish a section. The answers to all odd-numbered section exercises and to all the review exercises are provided at the back of your textbook.

The following list details our recommendations to help you to succeed in this course.

• Be prepared to practise. Do as many exercises as possible, keep a steady pace and review background material as you need it. You will note that we have assigned a lot of exercises. You may not be able to do them all, but we strongly recommend that you do as many as you have time for, and that you do not restrict yourself to the easier (earlier) exercises. Try to do all of the application problems.

• Make certain that you have the necessary background. We expect that you will have an understanding of basic algebra before you begin the course. Appendix A of your textbook (pp. 429–477) provides a review of basic algebra. We recommend that you begin by taking the self-test on pages 429–430, and review any concepts in which you are weak. If you require further explanations contact your tutor.

• Read your Study Guide and textbook effectively. The textbook is not a collection of solved problems; you are expected to understand the course material, and put it to use to solve the problems yourself. Hunting through a section to find a worked-out exercise that is similar to an assigned problem is totally inappropriate. Solving a mathematical problem requires an understanding of the concepts discussed.

  Never read mathematics without pencil and paper in hand. Read the corresponding assigned section before trying the exercises. You should treat the examples as exercises, and try to solve them without the authors’ help. Be prepared to check all the details as you read, and above all, read critically. Take nothing for granted.

  If you do not understand a statement, go back in the section, or to a previous section, to see if you missed or misunderstood something. If you still fail to understand a concept after puzzling over it for a while, mark the place, continue reading, and ask your tutor for help on that point.

• Prepare for the examinations. At the end of each unit, we present a “practice examination.” Pretend that each practice examination is a course examination that you are writing for credit: prepare for it carefully, and write it within the stated time limit.

  You are free to write these examinations under different conditions: closed book, open book, consulting your own notes, etc. If you consult any material, such as the textbook or Study Guide, take note of the time you spend in the consultation. This strategy allows you to determine whether you know where to find what you need. If you prepared notes, are they useful? Whatever you do, aim to be efficient with your time. Take note of the concepts you need to consult and make a point of finding them quickly, or better still, know them.

  Grade yourself based on the solutions provided in the “Student Solutions Manual” section of the textbook. Put yourself in the place of the marker and be critical. The marker will consider

  1. the general appearance of the examination. Are the answers neat and legible?
  2. whether the questions are answered in a logical manner.
  3. whether the explanations are well presented.
  4. whether the notation is used correctly.
  5. whether the student (you) clearly shows an understanding of the problem.

  Make sure to grade what is actually on the paper—not what you intended to do—because that is what the marker does. Learn from your mistakes, and ask yourself what is being tested.

  Note: Do not assume that the course examinations are identical, or even similar, to the practice examinations.

• Use good examination strategies when you write the examinations. Questions in the examinations aim to test whether the objectives of the course have been met. The grade assigned reflects what you know and how well you know it. The onus is on you to show your knowledge and mastery of the subject. You get credit for everything you do know, but a marker will not make guesses about what you may know.

  We strongly recommend that you begin by glancing over all the questions, and answering those you feel most confident about first. Leave to the end those questions that present special difficulty for you.

  You may be familiar with some of the questions in the examinations, but be prepared for unfamiliar questions as well. Do not panic when confronted with an unexpected or unfamiliar question; read the question carefully, and make sure you understand what is required. These questions are not necessarily difficult; rather, they are designed to test your understanding of concepts, and how well you can put them to use when solving problems.

  Note: Be aware that all questions in assignments and examinations are worth several points, because several steps must be taken to solve them. So please show all your work and provide proper justification for all your answers.