Math 55
Encyclopedia
Math 55 is a two-semester long first-year
undergraduate mathematics
course at Harvard University
. The official titles of the course is Honors Abstract Algebra
and Honors Real
and Complex Analysis
. (The official title was previously Honors Advanced Calculus and Linear Algebra.)
taught by Wilfried Schmid
), students take a quiz. In 1994, 89 students took the test given after 3 weeks: students scoring more than 50% on the quiz could enroll in Wilfried Schmid
's Math 55 (15 students), students scoring between 10 and 50% could stay in Benedict Gross
's Math 25 (55 students), and students scoring less than 10% were suggested to enroll in a lower-level course such as Math 21, multivariate calculus (19 students).
and Joe Harris; also, Harvard physics professor Lisa Randall
'84 and Harvard economics professor Andrei Shleifer
'82. Although a 2006 Crimson article alleged that only 17 women completed the class between 1990 and 2006, in fact 39 women completed 55a (the first of the two semesters), and 26 completed 55b. Math 25 has more women: in 1994–95, Math 55 had no women, while Math 25 had about 10 women in the 55 person course.
In addition to these professors, past students of Math 55 include Bill Gates
and Richard Stallman
. Gates said the experience of taking a class "where everybody had an 800 on their SAT
and 5 on their AP
" was a "neat experience".
Demographics of students taking this course over the years has been used to study causes of gender and race differences in the fields of mathematics and technology.
s. In 1994, students of Math 25 learned differential geometry using DoCarmo's book and calculus of variations
using C.H. Edwards's book.
From 2007 onwards, the scope of the course was changed to more strictly cover the content of four existing semester-long courses in two semesters: Math 25a (linear algebra) and Math 122 (group theory) in Math 55a; and Math 25b (calculus, real analysis) and Math 113 (complex analysis) in Math 55b. The name was changed to "Honors Abstract Algebra" and "Honors Real and Complex Analysis" to reflect this.
Freshman
A freshman or fresher is a first-year student in secondary school, high school, or college. The term first year can also be used as a noun, to describe the students themselves A freshman (US) or fresher (UK, India) (or sometimes fish, freshie, fresher; slang plural frosh or freshmeat) is a...
undergraduate mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
course at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
. The official titles of the course is Honors Abstract Algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
and Honors Real
Real analysis
Real analysis, is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real...
and Complex Analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
. (The official title was previously Honors Advanced Calculus and Linear Algebra.)
Description
The Harvard math department claims that "[t]his is probably the most difficult undergraduate math class in the country." Students begin the year by enrolling in Math 25, created in 1983 as a lower-level Math 55, and after 3 weeks of point-set topology and special topics (e.g., in 1994, p-adic analysisP-adic analysis
In mathematics, p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p-adic numbers....
taught by Wilfried Schmid
Wilfried Schmid
Wilfried Schmid is a German-American mathematician who works in Hodge theory, representation theory, and automorphic forms. He earned his Ph.D. at University of California, Berkeley in 1967 under the direction of Phillip Griffiths, and then taught at Berkeley and Columbia University, becoming a...
), students take a quiz. In 1994, 89 students took the test given after 3 weeks: students scoring more than 50% on the quiz could enroll in Wilfried Schmid
Wilfried Schmid
Wilfried Schmid is a German-American mathematician who works in Hodge theory, representation theory, and automorphic forms. He earned his Ph.D. at University of California, Berkeley in 1967 under the direction of Phillip Griffiths, and then taught at Berkeley and Columbia University, becoming a...
's Math 55 (15 students), students scoring between 10 and 50% could stay in Benedict Gross
Benedict Gross
Benedict Hyman Gross is an American mathematician, the George Vasmer Leverett Professor of Mathematics at Harvard University and former Dean of Harvard College....
's Math 25 (55 students), and students scoring less than 10% were suggested to enroll in a lower-level course such as Math 21, multivariate calculus (19 students).
Historical retention rate
In 1970, this demanding course covered almost four years worth of mathematics classes in two semesters, and therefore drew only the most dedicated students. In the class of 1970, only 20 of the 75 students who began the class finished it due to its difficulty. Similar drop-out rates were true for the class of 1976: "Seventy started it, 20 finished it, and only 10 understood it." and for the class of 2009: "51 students the first day, 31 students the second day, 24 for the next four days, 23 for two more weeks, and then 21 for the rest of the first semester."Notable alumni
Problem sets are expected to take from 24 to 60 hours per week to complete. Of those students who could handle the workload, many became math or physics professors, including many members of the Harvard Math Department such as Benedict GrossBenedict Gross
Benedict Hyman Gross is an American mathematician, the George Vasmer Leverett Professor of Mathematics at Harvard University and former Dean of Harvard College....
and Joe Harris; also, Harvard physics professor Lisa Randall
Lisa Randall
Lisa Randall is an American theoretical physicist and a leading expert on particle physics and cosmology. She works on several of the competing models of string theory in the quest to explain the fabric of the universe. Her most well known contribution to the field is the Randall-Sundrum model,...
'84 and Harvard economics professor Andrei Shleifer
Andrei Shleifer
Andrei Shleifer is a Russian American economist. From its inauguration in 1992 until it was shut down in 1997, Shleifer served as project director of the Harvard Institute for International Developments Russian aid project...
'82. Although a 2006 Crimson article alleged that only 17 women completed the class between 1990 and 2006, in fact 39 women completed 55a (the first of the two semesters), and 26 completed 55b. Math 25 has more women: in 1994–95, Math 55 had no women, while Math 25 had about 10 women in the 55 person course.
In addition to these professors, past students of Math 55 include Bill Gates
Bill Gates
William Henry "Bill" Gates III is an American business magnate, investor, philanthropist, and author. Gates is the former CEO and current chairman of Microsoft, the software company he founded with Paul Allen...
and Richard Stallman
Richard Stallman
Richard Matthew Stallman , often shortened to rms,"'Richard Stallman' is just my mundane name; you can call me 'rms'"|last= Stallman|first= Richard|date= N.D.|work=Richard Stallman's homepage...
. Gates said the experience of taking a class "where everybody had an 800 on their SAT
SAT
The SAT Reasoning Test is a standardized test for college admissions in the United States. The SAT is owned, published, and developed by the College Board, a nonprofit organization in the United States. It was formerly developed, published, and scored by the Educational Testing Service which still...
and 5 on their AP
Advanced Placement Program
The Advanced Placement program is a curriculum in the United States and Canada sponsored by the College Board which offers standardized courses to high school students that are generally recognized to be equivalent to undergraduate courses in college...
" was a "neat experience".
Demographics of students taking this course over the years has been used to study causes of gender and race differences in the fields of mathematics and technology.
Course content
Through 2006, the instructor had broad latitude in choosing the content of the course, and the course bore the title "Honors Advanced Calculus and Linear Algebra". For example, in 1970 by the second semester, students were learning about the differential geometry of Banach manifoldBanach manifold
In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic to an open set in a Banach space...
s. In 1994, students of Math 25 learned differential geometry using DoCarmo's book and calculus of variations
Calculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
using C.H. Edwards's book.
From 2007 onwards, the scope of the course was changed to more strictly cover the content of four existing semester-long courses in two semesters: Math 25a (linear algebra) and Math 122 (group theory) in Math 55a; and Math 25b (calculus, real analysis) and Math 113 (complex analysis) in Math 55b. The name was changed to "Honors Abstract Algebra" and "Honors Real and Complex Analysis" to reflect this.
External links
- Harvard Mathematics Department 21, 23, 25, or 55? – Harvard Math Freshmen Guide pamphlet
- Problem sets from Math 55 from 1999-2006
- 1983: Harvard Crimson, Feb 14, 1983
- 1994: In Math Department, It's Mostly Male, Harvard Crimson, Oct. 20, 1994
- 1999: http://www.thecrimson.com/article/1999/1/6/math-55-rite-of-passage-for/
- 2000: Math 55 student gets laid, considered for Fields Medal, Satire V (humor magazine), 2000
- 2006: Burden of Proof, December 2006, Harvard Crimson
- 2005: Math 55a – Noam ElkiesNoam ElkiesNoam David Elkies is an American mathematician and chess master.At age 14, Elkies received a gold medal with a perfect score at the International Mathematical Olympiad, the youngest ever to do so...
- 2009/10: Math 55a, Math 55b – Curtis McMullen
- 2010/11: Math 55a, Math 55b – Noam ElkiesNoam ElkiesNoam David Elkies is an American mathematician and chess master.At age 14, Elkies received a gold medal with a perfect score at the International Mathematical Olympiad, the youngest ever to do so...