📖 Overview
Alexander Barvinok is a mathematician known for his work in combinatorics, discrete geometry, and complexity theory. He currently serves as Professor of Mathematics at the University of Michigan.
Barvinok has made significant contributions to algorithmic counting problems and the computational aspects of geometric optimization. His most influential work includes developing polynomial-time algorithms for counting lattice points in fixed-dimensional polytopes, known as "Barvinok's algorithm."
His 2002 book "A Course in Convexity" is widely used in graduate mathematics programs and has become a standard reference in convex geometry. The text presents a systematic treatment of convex sets and functions in finite-dimensional spaces.
Barvinok received his Ph.D. from the University of Leningrad (now Saint Petersburg State University) in 1988. He has been recognized with several academic honors and has published extensively in leading mathematics journals, particularly in areas connecting discrete mathematics with continuous geometry.
👀 Reviews
Mathematics students and researchers view Barvinok's textbook "A Course in Convexity" as a comprehensive but challenging resource.
What readers liked:
- Clear organization and logical flow of concepts
- Detailed proofs and thorough explanations
- Strong focus on geometric intuition alongside rigorous theory
What readers disliked:
- Dense material requires significant mathematical maturity
- Some readers found exercises too difficult
- Limited worked examples compared to other textbooks
From Goodreads (3.67/5 from 6 ratings):
"Excellent resource but not for self-study" - Graduate student reviewer
"The proofs are elegant but require deep concentration" - Mathematics professor
From Amazon (4.5/5 from 8 reviews):
"Best treatment of convex optimization fundamentals"
"Problems are well-chosen but very demanding"
Mathematical reviews consistently note its value for graduate-level study but caution it may overwhelm undergraduate readers or those new to the subject.
📚 Books by Alexander Barvinok
A Course in Convexity (2002)
A graduate-level textbook covering convex sets, functions, and optimization methods in finite-dimensional spaces.
Integer Points in Polyhedra (2008) Examines methods for counting integer points in polyhedra, including generating functions, Ehrhart polynomials, and applications.
Combinatorics and Complexity of Partition Functions (2016) Explores partition functions in statistical physics and their connections to computational complexity theory.
Measure and Integration (2014) Presents measure theory and integration for graduate mathematics students, with emphasis on probability spaces and Lebesgue integration.
New Perspectives in Algebraic Combinatorics (1999) Collection of lectures on topics including polynomial spaces, symmetric functions, and representation theory.
Integer Points in Polyhedra (2008) Examines methods for counting integer points in polyhedra, including generating functions, Ehrhart polynomials, and applications.
Combinatorics and Complexity of Partition Functions (2016) Explores partition functions in statistical physics and their connections to computational complexity theory.
Measure and Integration (2014) Presents measure theory and integration for graduate mathematics students, with emphasis on probability spaces and Lebesgue integration.
New Perspectives in Algebraic Combinatorics (1999) Collection of lectures on topics including polynomial spaces, symmetric functions, and representation theory.
👥 Similar authors
Gilbert Strang writes textbooks on linear algebra and applied mathematics that share Barvinok's focus on mathematical fundamentals and clear explanations. His works contain similar geometric interpretations and concrete examples that bridge theory with applications.
Peter Cameron specializes in combinatorics and group theory with texts that present advanced concepts through systematic development. He employs a similar style of building from basic principles to complex theories while maintaining mathematical rigor.
Béla Bollobás produces works in combinatorics and graph theory that match Barvinok's level of mathematical sophistication and attention to proof techniques. His books feature comparable treatment of discrete mathematics topics with emphasis on modern research directions.
Martin Aigner writes on combinatorial theory and discrete mathematics using a comparable approach of mixing concrete examples with abstract concepts. His work contains similar attention to algorithmic aspects and computational methods in mathematics.
Richard Stanley creates texts on algebraic combinatorics and enumerative theory that parallel Barvinok's mathematical depth and systematic presentation style. His books contain similar combinations of classical theory with contemporary developments in the field.
Peter Cameron specializes in combinatorics and group theory with texts that present advanced concepts through systematic development. He employs a similar style of building from basic principles to complex theories while maintaining mathematical rigor.
Béla Bollobás produces works in combinatorics and graph theory that match Barvinok's level of mathematical sophistication and attention to proof techniques. His books feature comparable treatment of discrete mathematics topics with emphasis on modern research directions.
Martin Aigner writes on combinatorial theory and discrete mathematics using a comparable approach of mixing concrete examples with abstract concepts. His work contains similar attention to algorithmic aspects and computational methods in mathematics.
Richard Stanley creates texts on algebraic combinatorics and enumerative theory that parallel Barvinok's mathematical depth and systematic presentation style. His books contain similar combinations of classical theory with contemporary developments in the field.