Associate Professor & Assistant Chair
Areas of Expertise/Research
- Approximation Theory
- Complex Analysis
North Academic Center 8/133
My original area of research was Approximation Theory, focusing on extensions of Weierstrass' theorem on the uniform approximation of continuous functions by polynomials. More recently, I have written several articles on Complex Analysis, describing the interesting special properties of conformal mappings of closed domains.
The mathematical aspects of gambling have also been the background for several research articles, investigating the reciprocal relationship between the probability of winning an unfair game and the expected "duration of play". And a recently submitted article combines aspects of probability, complex analysis, and a famous unsolved problem of Frobenius.
Courses Taught and Administrative Work
Over the years, I have taught mathematics courses on virtually every level. Aside from our "service" courses - calculus, linear algebra and differential equations, which are required of most science majors - I have taught math majors' courses such as advanced calculus, probability, number theory, and numerical analysis. Most of these courses have not changed very much over the years, but numerical analysis has evolved a great deal with the increasing emphasis on computer science. In fact, aside from being a required course in our applied math track, numerical analysis has become one of the most popular courses for our many mathematics minors.
I have also especially enjoyed teaching the advanced undergraduate / graduate level of complex analysis. This subject has always fascinated me, and I had the opportunity to publish a textbook (Complex Analysis, Springer publishing) with the late world-renowned mathematician (and CCNY alumnus) D.J. Newman. In fact, a third edition was recently published as well as a Greek-language edition.
My administrative work revolved around my position as assistant chairman and majors' adviser. In these positions, which I have held for two decades, I have had the pleasure of guiding countless students through our variety of courses toward a major in one of the three tracks which we offer: pure math, applied math, and mathematics for future secondary education teachers. Many students have also taken independent study and honors courses one-on-one with our distinguished faculty members.
It has been a special pleasure following our alumni as they have gone on to graduate school and assumed positions in academia and in a large variety of corporations in the New York metropolitan area and throughout the country.
1) Bak and Newman, Muntz-Jackson Theorems in Lp and C[0,1], American Journal of Mathematics 94 (1972),437-457
2) Bak, On the Efficiency of General Rational Approximation, Journal of Approximation Theory 20 (1977), 46-50
3) Bak and Newman, Rational Combinations of x^k are Always Dense in C[0,1], Journal of Approximation Theory 23 (1978), 155-157
4) Bak, The Anxious Gambler's Ruin, Mathematics Magazine 74 (2001), 182-193
5) Bak, The Recreational Gambler: Paying the Price for More Time at the Table, Mathematics Magazine 80 (2007), 183-185
6) Bak, Ding, and Newman: Extremal Points, Critical Points and Saddle Points of Analytic Functions, American Mathematical Monthly 114 (2007), 540-546
7) Bak and Ding, Shape Distortion by Analytic Functions, American Mathematical Monthly 116 (2009), 143-150
8) Bak and Popvassilev, The Evolution of Cauchy's Closed Curve Theorem and Newman's Simple Proof, American Mathematical Monthly 124 (2017), 217-231
9) Bak, From Repeated Tosses of a Fair Die to the Renewal Theorem, submitted for publication (2020)