# MATH 432 History of Mathematics

#### (Fall 2017)

Instructor: Dr. Manil Suri

##### Updated Weekly Schedule may be found via Blackboard.

#### Basic Information

- Dr. Manil Suri, Math/Psych 419, (410) 455-2311, suri@umbc.edu,

office hours: MW 5:00-6:00 or by appointment - Lectures: MW 1:00-2:15, SOND 108
- Required Text: Fermat’s Enigma by Simon Singh
- Additional Texts:

(1) The History of Mathematics : An Introduction by David M. Burton

(2) A Mathematician’s Apology by G.H. Hardy

(3) A History of Mathematics by Merzbach and Boyer

(4) MacTutor History of Mathematics Archive (website) - Supplementary Texts (excerpts from these and other sources):

(1) Mathematics in Western Culture by Morris Kline

(2) Journey Through Genius: The Great Theorems of Mathematics by William Dunham

(3) Lost Discoveries – the Ancient Roots of Modern Science by Dick Teresi

(4) Is God a Mathematician? by Mario Livio

(5) Arcadia by Tom Stoppard

(6) Logicomix, An Epic Search for Truth by Apostolos Doxiadis and Christos Papadimitriou

(7) The Nothing That Is: A Natural History of Zero by Robert Kaplan - Syllabus: Selected readings.
- Prerequisites: MATH 301, ENGL 100.
- This is a WRITING INTENSIVE (WI) course.

#### Overview

We will use the popular text, “Fermat’s Enigma” by Simon Singh, as our starting point. This will launch us into various topics in mathematical history, which we shall explore through auxiliary reading assignments. Throughout, the standard textbook by Burton will serve as a key reference, with the book by Merzbach and Boyer and “The Story of Mathematics” website as supplementary ones. An important aspect of the course will be class discussions based on reading assignments, which in turn will help you write the essays on which you will be graded. This “active learning” format will facilitate a broad understanding of how mathematics evolved, along with additional depth in chosen topics of interest. In addition to the above books, we will read G. H. Hardy’s classic “A Mathematician’s Apology,” along with several other materials. The last part of the course will revolve around a creative project. A collaborative project will be offered, but you will also have an opportunity to propose your own project that involves some aspect of mathematical history.

#### Goals

Rather than a traditional format based solely on absorbing historical content, we will approach the history of mathematics as a multifaceted body of knowledge that plays a meaningful role in our present-day world. In addition to familiarizing ourselves with this knowledge, our goals will also be to:

(1) learn how historical advances have influenced mathematics as it is currently practiced.

(2) explore the role played by past conventions and cultures.

(3) understand how historical figures have shaped public perceptions of the subject.

(4) examine how historical influences may have shaped our own self-identity as mathematicians.

The “WRITING INTENSIVE” designation of the course will be a key guiding factor, leading to the following additional goals:

(5) hone writing ability (more generally, communication skills) particularly in terms of mathematical topics.

(6) explore how historical narrative (the “story” of mathematics) can be used to engage non-mathematical audiences.

#### Modules

The course consists of five modules (see Weekly Schedule for more):

**I. Fermat’s Enigma, or Math’s Greatest Hits: **Simon Singh’s book provides a historical narrative incorporating several engaging episodes from mathematics. We will pay attention to the audience(s) he aims at, particularly as topics become increasingly esoteric. Your first essay will be based on this book.

**II. Nothing was a problem for the Greeks: **We will look into the early development of mathematics and its foundations. Much is owed to the Greeks, especially the concept of proof. But some ideas, like the crucial step of defining zero (nothing) to be a number, were introduced and honed by non-Western cultures. Ascribing credit can still be a matter of controversy. Your second essay will be based on this material.

**III. Harnessing Infinity: **With the Renaissance (roughly the 14th through 17th centuries), Western mathematics started advancing again. One of the key developments, calculus, depended on understanding (and exploiting) the infinite and the infinitesimal – something Archimedes already had experimented with hundreds of years earlier. Cantor put infinity on firmer ground with his study of cardinality.

**IV. How to surprise a Mathematician: **Starting in the nineteenth century, mathematics was rocked by additional surprises beyond the multiplicity of infinity. Euclid’s parallel postulate could be replaced by a contradicting alternative and still lead to consistent geometries. Russell’s paradox showed sets could not be defined naively. Godel’s incompleteness theorem showed that Hilbert’s dream of finding a complete and consistent set of axioms for all of mathematics was impossible. The rise of computing in the twentieth century resulted in great advances and drastic changes.

**V. Why we are the way we are: **In these readings, we will look at how the culture of mathematics has evolved. One of the earliest, fundamental changes was the insistence on using proofs to justify theorems. But other entrenched attitudes have also been evolving: dividing mathematics into “pure” and “applied,” or thinking of certain parts as “beautiful” and others as “ugly.” Perhaps the greatest transformations have come in the relation of mathematics to other fields, and in the people, such as women and minorities, who make it their profession.

#### Assignments

There will be three types of homework assignments.

**Content**assignments will be web (Blackboard) based, and will be due by 1 p.m. on class days. These will generally test whether you have completed assigned readings before coming to class. In order to get a C or better in the course, you must achieve a minimum average score of 75% in these assignments. NOTE: In case there is a problem with Blackboard, let me know so alternative arrangements can be made for submission.**Writing**assignments will be in the form of essays based on issues discussed in class. Feedback (peer and/or instructor) will be provided, and there will be opportunities to resubmit them. These assignments, along with the project described below, will be designed towards satisfying UMBC WRITING INTENSIVE requirements. (There will be 2-3 main essays, along with possibly some shorter assignments.)- The
**project**will involve a creative element and will have to include some element of the history of mathematics. There will be a default collaborative effort you can participate in. Also, you will have opportunities to develop individual ideas as we go along (possibilities include a story, non-fiction piece, webpage, video, etc). There will be opportunities to present it to the class. Please note that our exam slot of Wed, Dec 20 from 1 to 3 pm is reserved for such presentations. Attendance is compulsory, and will be counted towards fulfilling your attendance requirement.

NOTE: All writing assignments (including writing pertaining to the project) must be submitted both via Blackboard and hard copy (unless other arrangements have been made). I would appreciate .docx files.

In addition to the above, there may be additional assignments given in class, which will be graded under the category of “Class work.”

#### Grading and Attendance

Your overall grade will be based on the following formula:

Content assignments: 10%

Writing assignments: 50%

Project: 25%

Class work: 15% (this will include 5 points for participation in discussion and 5 points for comments on other students’ work)

To get a C or better, you **MUST** obtain a minimum average of 75% in the content assignments. Once this is satisfied, the cut-off overall scores will be 90% for an A, 80% for a B, 65% for a C and 50% for a D.

**You are expected to attend all classes.** More than three absences without adequate cause will lead to a lowering of your grade. **If you anticipate more than five absences, consider dropping the class.**

#### Source Attribution, Plagiarism, and Academic Honesty

All sources must be clearly attributed (as a list of references) in essays (and other writing) submitted for grading. This list of references does NOT count towards the word count, so ensure your essay satisfies any length requirement without including it. Quotations must be clearly marked, and should ideally be limited to a sentence or two, rather than large chunks. **Do not try to pass off material written by others as your own. **This includes direct lifting of text but also opinions, descriptions, analysis and other material that has been cosmetically altered or paraphrased. When in doubt, attribute (or discuss with me or with your group). An assignment found to contain plagiarized material will be given zero credit, and incur other penalties in accordance with UMBC policy (see http://oue.umbc.edu/files/2015/09/iii-1.10.03.pdf, particularly the definition of plagiarism on page 3). **Please use one of the online plagiarism checkers before submitting your essays!**

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC’s scholarly community in which everyone’s academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. To read the full Student Academic Conduct Policy, consult the link above.

#### Accommodations for Disability

If you require accommodations for this class based on disability, please make an appointment to meet with me to discuss your SSS-approved accommodations. Please see http://my.umbc.edu/groups/sss/documents/838 for more information.