| Week | # | Sec | Topic | Homework (updated Friday morning) | Due dates/Forms/Material |
|---|---|---|---|---|---|
| Jan 27 |
1 |
1 1 1.2 1.3 |
Administrative
stuff. What is mathematics? Primitive counting; Positional and non-positional number systems. Mayan calendars.Babylonian number recording |
S1.2: 1 to 6, 11, 12, 13 S1.3: 1,2, 13, 14. (Assume that the Mayan is "honest" base 20) |
If you have been absent or will need to, please fill this
form (at any time of the semester). Timeline for the History of Mathematics (compiled by William H. Richardson of Wichita State University.) Number Systems Slides. That's mathematics (by Tom Lehrer) |
| Feb 3 |
2 |
1.3 2.1 2.2, |
Egyptian Arithmetic and multiplication The Unit Fraction Table |
S1.3: 3,4, 5, 17 S2.3: 1,2 Why does the Egyptian algorithm for multiplication work? |
Homework 0 (due Feb
4) Form for choosing the topic of the presentation (due Feb 4) Sample quiz. A blog of the British Museum about the Rosetta Stone The topics and dates for the presentation are here. Presentations start |
| Feb 10 |
3 |
2.3 2.4 |
The Unit Fraction Table Egyptian geometry |
S2.3: 3, 19,
20 S2.4: 1a, b (review formulas for areas and volumes) Roman numerals |
Google Form for outline, bibibliography and slides for presentations Google form for evaluating presentations |
| Feb 17 |
4 |
2.5 2.6 |
Babylonian Mathematics |
No quiz this week. | |
| Feb 24 |
5 |
3.1, 3.2, 3.3 |
Thales and Pythagoras |
"Decipher" Babylonian multiplication
tables. These problems (hint may not appear in the quiz). S2.5: 1. |
|
| March 2 |
6 |
3.3, 4.1, 4.2 4.4, 4.3 4.5 |
Euclid |
S3.2: 1. S3.3: 9, 15, 16, 17. And these problems |
Euclid's
elements website. The first six books of Euclid, by Oliver Byrne. Proclus about geometry and Euclid "Euclid alone has looked on Beauty bare." BY EDNA ST. VINCENT MILLAY |
| March 9 |
7 |
5.3, 5.5 |
Archimedes Apollonius |
S4.5: 1a, 1d,1e, 2 (review the formulas for areas
and volumes), And these problems S5.3: 1, 13, 14, 16 S5.5: 16 |
|
| March 16 |
Spring break | ||||
| March 23 |
|
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| March 30 |
8 |
7.3 |
Diophantus Islamic, Indian and Chinese mathematics during the "dark ages." (Early mathematics in India, The ancient chinese Nine Chapters) |
HW1 is here | The Google form for submitting the homework is here The topics and dates for recording the presentations are here. Note: I will arrange the exact time of presentation with each of you. The topic of the term paper is due on March 30th. Here is the term paper form. Here you'll find an outline of Chinese Mathematics by Prof.David E. Joyce. Here are the notes for the lecture of Tuesday March 31st (Ancient Chinese Square Root Algorithm). Here are the notes about Magic Squares. Here are the notes about Ancient Indian Mathematics. Here are a couple of questions about online teaching. |
| April 6 |
9 | 8.1, 8.2 |
al-Khwarizmi Kepler Fibnonacci (The Hindu-Arabic Numerals, Fibonacci's Liber Quadrarorum) Galileo Viete |
HW 2: Consists of 4 problems. Problems 1, 2 and 3"hidden" in the notes of the last week lectures. There is also an extra credit problem. Problem 4: Give a detailed justification of the Ancient Chinese Square Root Algorithm for 55225 discussed on March 31st (Check the steps of the algorithm in the slides and explain how they relate to the calculation we made in the begining, writing the answer as 100a+10b+c...). |
Log
in to JSTOR to find material for the final paper. Arc and half-chord app. The tentative bibliography of the paper is due on April 9nd. Here is the term paper form. Since access to libraries is not possible, you are not required to cite book sources. However, make sure that you use appropriate websites. Galileo's Arithmetic The slides of this week are here. if you want to zoom to my office hours, click here on Th 11:30 to 12:30. For office hours on Tu 11:30 to 12:30 and 9-10, you can do it through Blackboard. |
| April 13 |
10 | 9.1, 9.2, 9.3 |
Descartes (Inventing Cartesian
Geometry, The algebraic aspect of geometry). Cardano (Cardan's Solution of the Cubic Equation ) The development of probability (Pascal arithmetic triangle) |
HW3: Problems 1 to 4. Hidden in slides. Problem5. Here are pages of al-Khwarizmi. Some equations (stated in words) are numbered. Transcribe them to symbols. |
The outline of the paper is due on April 16th. Here is the term paper form |
| April 20 |
11 |
10.1 10.2 10.3 |
Newton and Leibniz. |
HW4: Problem
1, Problem 2: Section7.3, 1a and 1c. (Hint: check the book) Problem 3: Section 7.3, 2 (Hint: The solution is in the second part of the poem we worked on in class.) Problem 4: Section 7.3, 3a and 3d. |
The notes from this week are here.
A draft of the paper in PDF or Google Document must be submitted by April 23rd. Here is the term paper form |
| April 27 |
12 |
11.1 11.2 11.3 11.4 |
Number theory from Fermat to Euler and Gauss. ((Numbers perfect and not so perfect, Fermat's Arithmetica)Euler's life and contributions, The legacy of Gauss: Congruence Theory) | HW 5: 8.4: 1, 3, 11, 13 Use Fermat method to determine the subtangent of the curve y=x^3, at a point P=(x,x^3). Also: Read this article about Newton and the plague. |
Here
is the article about the history of the Prime Number Theorem. if you want to zoom to my office hours, click here on Th 11:30 to 12:30. For office hours on Tu 11:30 to 12:30 and 9-10, you can do it through Blackboard. |
| May 4 |
13 |
Review - Non-euclidean geometries Map coloring problems |
HW6 (the last!) 10.1: 3, 4, 6. 10.3: 2, 4. . |
Term papers are due on Thursday May 7th. Late papers will not be accepted. Read the instructions in the course syllabus. The ONLY WAY of submitting term papers is through Blackboard->Assignments in PDF form. (Make sure you export your paper to PDF before uploading it). |