History of Mathematics for Secondary School Teachers

HISTORY OF MATHEMATICS MATH -350

Instructor Dr. Lev V. Idels

VIU Mathematics Department

Fall 2015

Location: Nanaimo Campus

Office: 359/204 Ph: 7533245 Local 2429

This course is an introduction to the history of mathematics as the evolution of mathematical thought from primitive counting to the ideas of the 21^st century. Prerequisite: Six credits of 200-level Math with a min. "C" in each course.

This course is great for all students (future teachers or otherwise), who like mathematics and want to learn its history and development. For example, future math teachers who will want to:

Inspire pupils (Hey class: Do you know that this problem was solved by 26-year old kid?)

Make some relaxation during class (Hey class: Do you know the history of a blackboard?)

Show the power of modern knowledge (Hey class: Now you could get this result in 5 minutes, but 200 years ago smart people years to get it!)

Aims of the Course

Present the results that have made what mathematics is today and meet the mathematicians that created them. Give you a deeper understanding of mathematical concepts by learning how and why those concepts arose; knowledge of mathematical symbols and constants. Guide how you might use the history of mathematics in your own future career. Improve your written and spoken communication skills.

Course Outline (tentative)

Week 1-3 Ancient Mathematics

Number Systems: Babylonian, Roman, Greek, and Arabic

Week 4 History of Math Symbols and Constants

Week 5-9 Brilliant Discoveries: Ten Great Theorems of Mathematics

Pythagorean Theorem

The Impossibility of Trisecting the Angle and Doubling the Cube

Quadrature of a Circle

The Independence of the Parallel Postulate and Non-Euclidean Geometry

Fermat’s Great and Little Theorems

Fundamental Theorem of Algebra

Insolvability of General Higher Degree Equations

Fundamental Theorem of Integral Calculus

Prime Number Theorem

Four-Color Theorem

Week 10 Women in Mathematics

Week 11 Class Presentations

Week 12-13 Modern Mathematics: From Hilbert to Whiles, Mandelbrot and Navier-Stokes.

Text: Reading List of Math History Books @VIU Library

Lecture notes will not, in general, be provided. It is up to the student to attend class, so I encourage you to attend lectures regularly.

The course assessment will be based on the following:

25% Five in class quizzes. In Class Quiz . The in class quizzes will consist of questions (covered in class) trying to determine whether you were following the course. You rarely will be responsible for exact dates of events, but you should have an idea of how events developed in time.

Quiz #1

Quiz #2

Quiz #3
Quiz #4
Quiz # 5

20% 10 take home quizzes. Sample of Take Home Quiz . The take home quizzes determine your ability to work with external sources, such as the internet and library books.

35% Final examination. The final examination requires some memorization of dates and facts and a good broad overview of the course.

20% Presentation.

List of topics for presentations:

1. Geometric solutions of polynomial equations.

2. The concept of infinity.

3. Kellen Myers' list of mathematicians who died in "unpleasant" ways.

4. How students learn history of Mathematics in the classroom.

5. History of Math paradoxes.

6. Hundred formulae for One tiangle.

7. Four proofs of the Intermediate-Value Theorem.

8. Mechanical curves.

9. Islamic Mathematics and mathematicians.

10. Twenty three problems of D. Hilbert.

12. Zeno's paradoxes.

13. Math lyrics.

14. History of teaching Math in Canada.

15. Paul Erdös and the Erdős Number .

16. The Most famous mathematicians on Earth.

17. Most famous Canadian mathematicians.

18. Biography of the winners of the Fields Medal.

19. A Most-wanted list of seven of the most intractable Math problems in the world.

20. What’s new in Mathematics today?

21. Grigory Perelman, the Maths genius who said No to $1m.

22. Mathematician jokes.

23. Natural born mathematicians? Journey to the past.

24. Unknown mathematicians that makes history of Mathematics.

25. Fictitious mathematicians.

Presenting your talk is a new and sometimes frightening experience for students to present a talk in front of a class. Relax, and look on it as a unique opportunity to talk about something on which you know more than anyone else, including the teacher. The presentations will be worth 20% of the overall mark in the course. They will be graded on:

1. Knowledge of material.

2. Organization of material: what you choose to cover, and how you choose to organize it.

3. Clarity and style of presentation: speaking clearly, looking at audience, giving clear explanations, etc.

4. Duration: if you end within the time span given, you get full marks for this category; otherwise, you lose marks. You might want to build some flexibility into the end of your presentation so you can adjust on the fly.

Note that knowledge of material is just a small part of the grade. The presentation itself is much more important. In the week before your presentation, cull this material to the bare minimum needed to explain the essence of the text, and practice it either before your friends or in front of a mirror.

Interesting webpages

Solve if you dare: Unsolved Problems in Mathematics

How Math makes you rich https://plus.maths.org/content/how-maths-can-make-you-rich-and-famous

http://www.businessinsider.com/math-problems-that-you-can-solve-to-earn-prizes-2013-7

Chronological List of Mathematicians: http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html

Look who is today’s mathematician: http://www-history.mcs.st-and.ac.uk/history/Day_files/Now.html

Grading System

%	90-10	85-89	80-84	76-79	72-75	68-71	64-67	60-63	55-59	50-54	0-49
Letter Grade	A+	A	A-	B+	B	B-	C+	C	C-	D	F
Grade Point	4.33	4.00	3.67	3.33	3.00	2.67	2.33	2.00	1.67	1.00	0.00

Quiz absence, homework (take home quiz) handed in late or not at all: If you are unable to attend the in class quiz, you must notify the instructor in advance with a legitimate excuse or provide professional documentation of any medical emergency etc. within two days of the exam date. In either of these two cases (and only in these two cases), the weight of the final exam will be increased to compensate for the missed quiz. Undocumented absence from the quiz and homework assignments handed in late or not at all will be given a score of zero.

Re-marking requests: If you feel that a returned quiz is incorrectly marked, you can appeal that grade by writing a note that details your concern, attaching it to the quiz, and resubmitting.

Class etiquette: Use of cell phones (including text messaging, answered or unanswered ringing etc.) during class is highly inappropriate and disrespectful to both the instructor and fellow students. Chit chat with neighbours, even when whispered, is equally unacceptable.

HAVE FUN!