MAT 336  History of Mathematics  

Spring 2018  TuTh 2:30-3:50pm Physics P-112

Instructor: Ljudmila Kamenova

e-mail: kamenova@math.stonybrook.edu
Office: Math Tower 3-115
Office hours: Wednesdays 11am-12 in the MLC, 12-2pm in Math Tower 3-115


Grader: David Hu, e-mail: david.hu AT stonybrook.edu
Grader's office hours: Mondays 2:30 - 3:30pm in Math Tower 2-122; 5 - 7pm in the MLC

Syllabus: We shall study the history of mathematics, from the earliest times to the beginning of the 20th century. Special attention will be paid to the contributions of the Inca, Mayans, Babylonians, Greeks, Hindus, Arabs, Chinese and to the subsequent later European developments into the modern era.

Prerequisites: MAT 200 or MAT 203 or MAT 307 or AMS 261

Required Text: David M. Burton, The History of Mathematics: An Introduction, 7th edition, McGrawhill 2011.

Recommended Text: William Dunham, Journey Through Genius, Penguin 1990.

See also Jenia Tevelev's webpage.

Grading: Weekly Quizzes: 30%, Class Presentation: 20%, Term Paper: 50%

Suggested reading from the textbooks will be assigned each week. The weekly quizzes will be over what has been discussed in class during the previous couple of weeks, as well as the reading.

Each student will give a 15 minute oral presentation in front of the class over a topic assigned by the instructor. After the presentation, there will be a 5 minute class discussion, in which the other students can ask questions, or make comments about the presentation.

Each student will write a term paper of 15-20 pages on a topic that must be approved by the instructor. The paper should be typed double spaced, any size font or stype. The term paper will be graded on its content, as well as on how well it is written. The term paper should be handed in by Tuesday, May 1, in class. Late papers cannot be accepted.

There will be no final exam.

Topics for the in-class presentations:

Quipus (Peruvian Knots) by Carmen F. on 2/6; Chinese Bamboo Rods by Ya Liu on 2/6; Mayan Calendar by Julia V. on 2/8; Babylonian Clay Tablets by John C. on 2/8; Rhind Papyrus and the Rosetta Stone by Anthony N. on 2/13; Greek Attic numerals by Dylan M. on 2/15; Roman numerals by Rachael O. on 2/15; Pythagoreans by Sam Z. on 2/20; Hippocrates and the quadrature of the circle by Jasmin T. on 2/20; Eratosthenes' measurement of the Earth by Dan G. on 2/22; Equivalent versions of Euclid's 5th postulate by Branden C. on 2/27; Construction of a pentagon by Sayan S. on 2/27; Heron's formula for the area of a triangle by Wenjing W. on 3/1; Apollonius and conics by Ricky S. on 3/6; Ptolemy's Almagest by Chaofan Y. on 3/6; Diophantus' Arithmetica by Albert S. on 3/8; Pappus by Xinyu X. on 3/8; Roman mathematics by Robert A. on 3/20; al-Khowarizmi by Irene S. on 3/20; Hypatia by Hao Y. on 3/22; Nine Chapters of the Mathematical Art by Qianzhu W. on 3/22; Fibonacci's Liber Abaci by Daniel W. on 3/27; Founding of Universities by Chen L. on 3/27; Francois Viete by Hannah K. on 3/29; Napier and Logarithms by Yijing Zhang on 4/3; Tycho Brahe and Kepler by Lydia C. on 4/3; Galileo Galilei by Heeseong K. on 4/5; Desargues Theorem by Christopher S. on 4/10; Leibniz vs Newton by Tom S. on 4/10; B. Pascal by Kyujin C. on 4/12; D. Bernoulli by David D.-S. on 4/12; Lagrange by Shihao T. on 4/17; A. Cauchy by Yanchao S. on 4/17; Lobachevsky by Hubert P. on 4/19.

Homework (not to be handed in): Here are some practice problems for the weekly quizzes.

HW 1. Problems 1-5, 13, 14, 15 from Section 1.3 in Burton's book.

HW 2. Problems 1, 2, 9, 11 from Section 2.5; Problems 1, 2 from Section 2.6 in Burton's book.

Quiz 1 on Thursday, Feb 8, at the end of class. It is based on HW 1 and 2.

HW 3. Problems 1, 2, 3 from Section 2.3; Problems 8, 11 from Section 1.2 in Burton's book.

Quiz 2 on Thursday, Feb 15, at the end of class. It is based on HW 3.

HW 4. Problems 1, 5, 8, 15, 16 from Section 3.3; Problems 11, 12 from Section 4.2, Problems 15, 16 from Section 4.3 in Burton's book.

Quiz 3 on Thursday, March 1, at the end of class. It is based on HW 4 and the lectures on Chapter 4.

HW 5. Problems 13, 14, 16 from Section 5.3; Problems 1, 2, 10, 11 from Section 5.5 in Burton's book.

Quiz 4 on Thursday, March 8, at the end of class. It is based on HW 5 and the lectures on Chapter 5.

HW 6. Problems 1, 2, 3 from Section 6.3; Problems 3 (a,b), 5, 8 from Section 7.3 in Burton's book.

HW 7. Problems 12, 13 from Section 8.1; Problems 1, 2, 6, 7 from Section 8.2 in Burton's book.

Quiz 5 on Thursday, March 29, at the end of class. It is based on HW 7.

HW 8. Problems 1, 3, 4 from Section 8.3; Problems 1, 3, 4, 5 from Section 8.4 in Burton's book.

Quiz 6 on Thursday, April 5, at the end of class. It is based on HW 8.

HW 9. Problems 1(a,c), 2, 9, 10(b,c) from Section 9.2; Problems 1, 4(a,b), 11(a,b), 14 from Section 9.3 in Burton's book.

Quiz 7 on Thursday, April 19, at the end of class. It is based on HW 9.

HW 10. Problems 2, 4, 11 from Section 10.2; Problems 4, 6, 8, 12 from Section 10.3 in Burton's book.

Quiz 8 on Thursday, April 26, at the end of class. It is based on HW 10.

Writing Requirement: Successful completion of MAT 336 with a C or better satisfies DEC H and the expository portion of the upper-division writing requirement for the mathematics major, as well as the STAS, WRTD, and SPK objectives in the Stony Brook Curriculum. The learning outcomes corresponding to the SBC objectives are:

Learning Outcomes for "Understand relationships between Science or Technology and the Arts, Humanities or Social Sciences (STAS)"
1. Apply concepts and tools drawn from any field of study in order to understand the links between science or technology and the arts, humanities or social sciences.
2. Synthesize quantitative and/or technical information and qualitative information to make informed judgments about the reciprocal relationship between science or technology and the arts, humanities or social sciences.

Learning Outcomes for "Speak Effectively before an Audience (SPK)"
1. Research a topic, develop an oral argument and organize supporting details.
2. Deliver a proficient and substantial oral presentation for the intended audience using appropriate media.
3. Evaluate oral presentations of others according to specific criteria.

Learning Outcomes for "Write Effectively within One's Discipline (WRTD)"
1. Collect the most pertinent evidence, draw appropriate disciplinary inferences, organize effectively for one's intended audience, and write in a confident voice using correct grammar and punctuation.

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