MATH 336 Advanced Algebra

MATH 320 – History of mathematics: Past-1600 Summer 2008 Section 01: MTWU 3:40-5:30 pm Instructor: Lucian M. Ionescu Contact Info: WIH 336, 438-7167; [email protected]; www.ilstu.edu/~lmiones/mat320.htm Office Hours: TBA or by appointment at other times. Text: A History of Mathematics: An Introduction, by Victor Katz, 2nd ed., 1998. Content: In this course, students will study the development of mathematics from the growth of algebraic reasoning of early Mesopotamia and the geometry of ancient Greece through the mathematics of the Renaissance. We will learn how mathematics was discovered and developed, and why. Mathematics is at the same time art and science; the interactions with other sciences shaped the problem solving process into mathematical modeling. The emphasis will be on Greek geometry and growth of algebraic notation and reasoning during renaissance. Prerequisites: MAT 147 recommended. Course Format: You are responsible for reading assignments, and this is not a trivial task. The reading assignment is to be completed before the next scheduled meeting of the class. During the class, we will discuss the main people in the forefront together with the corresponding mathematics. Written outlines of the corresponding reading assignment are due the next class and will be used as a base of discussions. Homework: Solutions for the exercises stated in class, consisting in details and/or proofs supplementing the class explanations, are expected the next class period, but will be collected on a weekly basis. Projects: There will be one project to be concurrently developed during the course, with weekly submissions and revisions. The final submission as an e-mail attachment should be in Rtf file format (Rich Text Format); the weekly drafts will be accepted also in MS Word 2002 or Txt formats. The Project/Essay: “Mathematics: art or science?” Discuss the mathematics discovered from the point of view of its roots and mathematician’s motivation; was it discovered out of pure curiosity (“math as an art”) or prompted by a practical need (“math as a science”)? Even if discovered out of curiosity, explain its later role within mathematics itself or how it was used by another science. Other “math events” arose from the need to model reality as investigated by another science, so it is predominantly “math as a science”. There is no right/wrong approach here; we will discuss your project as we go and you will develop it towards a final version to be submitted the last day of class. Feel free to take a personal attitude and spend more time on your favorite kind of math and problems. Graduate Credit: For graduate credit, research the connection between the material presented and the current curriculum (elementary/middle/high school levels and mathematics areas). Plan ahead; e.g. “I will tell this nice story in this / that class” or how math education could benefit from incorporating the historical roots and motivation in the curriculum etc. Exam: There will be one Final Exam; it will be based on the material covered, class discussions and problems solved as part of the homework (More info on the study guide). Evaluation: Grades will be based on the following points: Class activities (Attendance and participation 100, outlines 100): 200 Homework: Project (4 weekly submissions x 50 points each) 200 Final exam 100 Total 500 points. The grading scale is based on: A [90-100%], B [80-90%), C [70-80%), D [60,70%), F [0,60%). N.B.: Students who believe they may need accommodations in this class/program are encouraged to contact the Disability Access Center as soon as possible to better ensure that such accommodations are implemented in a timely fashion.

“Warning: Plagiarism and cheating are serious offenses. Penalties can range from a minimum of a zero grade on the invalid instrument to expulsion from the University”

Suggestions for Learning (Mathematics)

Make an outline: For each assigned section of the text, make an outline containing a description of the major concepts and procedures. As you are making this outline, make a list of questions you want to ask your study partner or instructor.

Do the assignments: Work on your project each day. The best strategy is to write the outlines in a file and use it to develop your Project on a daily basis. Develop the list of questions to ask your study partner or instructor.

History of Mathematics: Past-1600

HW Homework: develop the Project No. Date Chapter / Period & Exercises1 1 M 6/16 Introduction www.ilstu.edu/~lmiones/320Intro.doc T 1 Ancient Math and Pythagorean Theorem Beginning of Greek math: Pythagoras, W 2.1-2.3 Plato, Aristotle, Zeno Th 2.4-2.5 Euclid and the Elements 2 M 6/23 3 Archimedes and Apollonius (conics) Hipparchus and trigonometry T 4.1-4.2 Ptolemy: math methods and astronomy 4.3 Menelaus and Heron W 5.1 Nichomachus and number theory, 5.2 Diophantus and algebra Th 5.3 Pappus and analysis 3 M 6/30 6, 7 China, India T 8 Islam, Europe and other places Algebra (the cubic equation), W 9.1-9.3 complex numbers Th 9.4 Viete and algebraic equations 4 M 7/7 10.1-10.2 Perspective, geography and navigation Astronomy and trigonometry, logarithms, 10.3-10.5 T kinematics W Review Th Final exam

1 Exercises: http://www.ilstu.edu/~lmiones/320Exercises.doc