Department of Mathematical Sciences,
Northern Illinois University

MATH 302 Spring 2013
DuSable Hall 302
Monday, Wednesday 4 - 5:15
Richard Blecksmith

| Catalogue description | Prerequisite | Course Objectives | Syllabus | Withdrawal | Grading | Room | Instructor | Text Handouts | Sample Exams | Spring Break | Final Exam | Some advice |

INTRODUCTION TO GEOMETRY (3 semester hours)

Basic concepts in plane and solid geometry, measurement, congruence and similarity, constructions, coordinate geometry, transformations, tessellations, topology, and selected topics.

Not used in major or minor GPA calculations for mathematical sciences majors or minors. It is a required course for the Minor in Mathematics Education.

PREREQUISITE: MATH 229 or consent of department.

COURSE OBJECTIVES:

SYLLABUS: The course will cover most of Modules 1-8 of the text.

WITHDRAWAL: The last day for undergraduates to withdraw from a full-session course is Friday, March 7.

GRADING: Grades will be assigned on the basis of 500 points, as follows:

2 hour exams worth 100 points each
Homework, attendance, and writing assignments: 150 points total
Total: 350 points

TIME and PLACE:

  • Section 1, 4:00-5:15 Mon Wed DU 302

    INSTRUCTOR:

  • Richard Blecksmith
    Office: Watson Hall 355
    Email: richard@math.niu.edu
    Phone: 753-6753
    Office Hours: Mon, Wed 3-4 and Mon 1-2

    HANDOUTS FROM THE TEXT: The text

    Math 302 Introduction to Geometry:    Lecture Notes
    by Richard Blecksmith
    is available online.
    NOTE: Each module is in PDF format, so you will need Adobe's Acrobat Reader which is a free and useful download. Click on the above link to get the latest version of the Acrobat Reader.
    Please download a copy of Module 1 Section 1 for yourself.
    If you like, I can supply a paper punch to use these notes in a 3-ring binder.
    The other sections and modules will become available as we get to them in class.
    Overview (Handed out in class)
    Module 1. Infinity
    Section 1. The 999 Question
    Section 2. Hotel Infinity
    Section 3. The Cantor Set
    Section 4. Fermat's Method of Descent
    Section 5. Geometric Series
    Module 2. Logic
    Module 3. Topology
    Module 4. Foundation for Geometry
    Part 1. Basic Axioms of Lines and Points
    Part 2. Angles and Triangles
    Part 3. Congruence and Perpendiculars
    Part 4. Parallels and Angle Sum
    Module 5. Topics in Geometry
    Module 6. Regular Polygons and Circles
    Module 7. Non-Euclidean Geometry
    Module 8. Constructions

    SAMPLE EXAMS: I will try to make some old exams available to you.

    SPRING BREAK: Spring Break is from March 10 through March 18, immediately after the last day to withdraw from the course, Friday March 9.

    FINAL EXAM: The Final Exam is scheduled for 4:00 - 5:50 p.m., Wednesday, May 14, 2008. (Note the new date since final exams have been moved back by a week.) The room is probably the regular classroom, DU 348. If it changes, you will be told at the end of the semester.

    ADVICE:

    About the text: In a way this text will be one of the easiest math books you've ever read. Many of the sections are written in dialogue form, with a minimum of formulas and a lot of space spent on simple explanations. Let's face it, most math students don't read the textbook, except for the exercises and possibly the examples - to be read only when you get stuck on the exercises. Hopefully this book is different. Try reading it and see.

    In another way this text will be one of the most challenging math books you might have ever been exposed to. It expects you to think and thinking - especially in mathematics - is hard work. But it can also be fun. That's why the cross-word puzzle is often found near the comics in the newspaper. Thinking isn't so bad if you believe that what you're thinking about is worth the effort. The difference between mathematicians and the rest of the world is that mathematicians actually like thinking about math. It may surprise you to discover that mathematics is not as boring and humdrum as you might believe. Many people who dislike the subject can still get interested in topics such as infinity, chaos theory, space-filling curves, and logical paradoxes. In this course you will discover that not all infinities are the same; that you can have curves with a finite area, but an infinite perimeter; that you can reorder the points on the number line so that they do not take up any length.

    One warning: Not all the questions posed in the text are answered for you; not all the theorems and facts are proved for you. You will have to work many of them out yourself - possibly with the help of your instructor or classmates. This is not your typical "how-to" course. Your job, as a student, should not be rote utilization of formulas, but rather reasoning, thinking, and possibly discovering.

    Advice about the course: Perhaps the single most important factor in your success in this course is your study habits . Think of learning math as "working out" in the gym. Study at least 3 times per week; do not wait until the day before the exam. Learn mathematics like you would learn a language. Work on the concepts until they make sense. Don't just memorize facts and then forget them a few weeks later. Master as many homework problems as you can - beyond just getting a correct answer. Always come to class! While you're there, listen, think, and ask questions.

    Last update: Feb 4, 2008