Peter Abramenko headshot

Peter Abramenko

Unit: College of Arts and Sciences
Department: Department of Mathematics
Office location and address
306 Kerchof Hall
141 Cabell Dr
Charlottesville, Virginia 22904
MATH 3000: Transition to Higher Mathematics
Credits: 4
Covers basic concepts with an emphasis on writing mathematical proofs. Topics include logic, sets, functions and relations, equivalence relations and partitions, induction, and cardinality. Prerequisite: Math 1320; and students with a grade of B or better in Math 3310, 3354, or any 5000-level Math course are not eligible to enroll in Math 3000.
MATH 3310: Basic Real Analysis
Credits: 4
A rigorous development of the properties of the real numbers and the ideas of calculus including theorems on limits, continuity, differentiability, convergence of infinite series, and the construction of the Riemann integral. Students without prior experience constructing rigorous proofs are encouraged to take Math 3000 before or concurrently with Math 3310. Prerequisite: MATH 1320.
MATH 4651: Advanced Linear Algebra
Credits: 3
Review of topics from Math 3351 including vector spaces, bases, dimension, matrices and linear transformations, diagonalization; however, the material is covered in greater depth with emphasis on theoretical aspects. The course continues with more advanced topics including Jordan and rational canonical forms of matrices and introduction to bilinear forms. Additional topics such as modules and tensor products may be included. Prerequisite: MATH 3351
MATH 4652: Introduction to Abstract Algebra
Credits: 3
Structural properties of basic algebraic systems such as groups, rings, and fields. A special emphasis is made on polynomials in one and several variables, including irreducible polynomials, unique factorization, and symmetric polynomials. Time permitting such topics as group representations or algebras over a field may be included. Prerequisites: MATH 3351 or 4651 and MATH 3354 or permission of the instructor.
MATH 7600: Homological Algebra
Credits: 3
Examines categories, functors, abelian catqegories, limits and colimits, chain complexes, homology and cohomology, homological dimension, derived functors, Tor and Ext, group homology, Lie algebra homology, spectral sequences, and calculations. Prerequisite: MATH 5770.
MATH 7753: Algebra III
Credits: 3
Studies the Wedderburn theory, commutative algebra, and topics in advanced algebra. Prerequisite: MATH 7751, 7752, or equivalent.
MATH 7754: Algebra IV
Credits: 3
Further topics in algebra.
MATH 7755: Problems in Algebra
Credits: 3
A continuation of the theory presented in MATH 7751 and 7752 intensively training students to apply the theory to proving theorems in algebra, especially in preparation for the General Examination in Algebra. Problems are based on those from past General Exams. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students.
MATH 8600: Commutative Algebra
Credits: 3
The foundations of commutative algebra, algebraic number theory, or algebraic geometry.
MATH 8998: Non-Topical Research, Preparation for Research
Credits: 1–12
For master's research, taken before a thesis director has been selected.
MATH 9998: Non-Topical Research, Preparation for Doctoral Research
Credits: 1–12
For doctoral research, taken before a dissertation director has been selected.
MATH 9999: Non-Topical Research
Credits: 1–12
The Mathematics Colloquium is held weekly, the sessions being devoted to research activities of students and faculty members, and to reports by visiting mathematicians on current work of interest. For doctoral dissertation, taken under the supervision of a dissertation director.