## Manuel Reyes

Assistant Professor of Mathematics

### Contact Information

mreyes2@bowdoin.edu

207-725-3574

Mathematics

Searles Science Building - 104

### Teaching this semester

### MATH 1750. Integral Calculus, Advanced Section

**Manuel Reyes**

A review of the exponential and logarithmic functions, techniques of integration, and numerical integration. Improper integrals. Approximations using Taylor polynomials and infinite series. Emphasis on differential equation models and their solutions. An average of four to five hours of class meetings and computer laboratory sessions per week. Open to students whose backgrounds include the equivalent of Mathematics 1600 and the first half of Mathematics 1700. Designed for first-year students who have completed an AB Advanced Placement calculus course in their secondary schools.

### MATH 2702. Rings and Fields

**Manuel Reyes**

An introduction to algebraic structures based on the study of rings and fields. Structure of groups, rings, and fields, with an emphasis on examples. Fundamental topics include: homomorphisms, ideals, quotient rings, integral domains, polynomial rings, field extensions. Further topics may include unique factorization domains, rings of fractions, finite fields, vector spaces over arbitrary fields, and modules. Mathematics 2502 is helpful but not required.

### Education

- Ph.D. University of California, Berkeley
- B.S. Westmont College

### Research Interests

Algebra: ring theory, module theory, noncommutative (algebraic) geometry, operator algebras, category theory, and interactions between these topics.

### Selected Publications

- Manuel L. Reyes,
*A prime ideal principle for two-sided ideals*, Comm. Algebra 44 (2016), no. 11, 4585-4608. - Manuel Reyes, Daniel Rogalski, and James J. Zhang,
*Skew Calabi-Yau algebras and homological identities*, Adv. Math. 264 (2014), 308-354 - Chris Heunen and Manuel L. Reyes,
*Active lattices determine AW*-algebras*, J. Math. Anal. Appl. 416 (2014), no. 1, 289-313. - Chris Heunen and Manuel L. Reyes,
*Diagonalizing matrices over AW*-algebras*, J. Funct. Anal. 264 (2013), no. 8, 1873-1898. - Manuel L. Reyes,
*Obstructing extensions of the functor Spec to noncommutative rings*, Israel J. Math. 192 (2012), no. 2, 667-698. - T.-Y. Lam and Manuel L. Reyes,
*A Prime Ideal Principle in commutative algebra*, J. Algebra 319 (2008), no. 7, 3006-3027.

A complete list of publications can be found at my personal page.

Personal page: http://bowdoin.edu/~reyes/