CasalainaMartin performs research in mathematics. He is an algebraic geometer with a broad range of interests. His research focuses on curves, abelian varieties, vector bundles, and moduli spaces.
keywords
Algebraic geometry, curves, abelian varieties, vector bundles, and moduli spaces
MATH 2001  Introduction to Discrete Mathematics
Primary Instructor

Spring 2020 / Spring 2022
Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Credit not granted for this course and MATH 2002.
MATH 2130  Introduction to Linear Algebra for NonMathematics Majors
Primary Instructor

Summer 2018 / Summer 2019 / Spring 2021 / Fall 2022
Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who do not plan to major in Mathematics. Degree credit not granted for this course and MATH 2135 or APPM 3310. Formerly MATH 3130.
MATH 2135  Introduction to Linear Algebra for Mathematics Majors
Primary Instructor

Spring 2018 / Fall 2020
Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who plan to major in Mathematics. Degree credit not granted for this course and MATH 2130 or APPM 3310. Formerly MATH 3135.
MATH 2300  Calculus 2
Primary Instructor

Fall 2018
Continuation of MATH 1300. Topics include transcendental functions, methods of integration, polar coordinates, differential equations, improper integrals, infinite sequences and series, Taylor polynomials and Taylor series. Department enforced prerequisite: MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C). Degree credit not granted for this course and APPM 1360.
MATH 3140  Abstract Algebra 1
Primary Instructor

Summer 2020 / Summer 2021 / Fall 2021 / Fall 2022
Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields.
MATH 3850  Seminar in Guided Mathematics Instruction
Primary Instructor

Fall 2018
Provides learning assistants with an opportunity to analyze assessment data for formative purposes and develop instructional plans as a result of these analyses. These formative assessment analyses will build on the literature in the learning sciences. Students gain direct experiences interacting with the tools of the trade, especially with actual assessment data and models of instruction. May be repeated up to 3 total credit hours. Restricted to learning assistants in Math.
MATH 4140  Abstract Algebra 2
Primary Instructor

Spring 2020
Explores some topic that builds on material in MATH 3140. Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Same as MATH 5140.
MATH 6170  Algebraic Geometry
Primary Instructor

Spring 2021
Introduces algebraic geometry, including affine and projective varieties, rational maps and morphisms and differentials and divisors. Additional topics might include Bezout's Theorem, the RiemannRoch Theorem, elliptic curves, and sheaves and schemes. Department enforced prerequisite: MATH 6140. Instructor consent required for undergraduates.
MATH 6290  Homological Algebra
Primary Instructor

Spring 2018
Studies categories and functors, abelian categories, chain complexes, derived functors, Tor and Ext, homological dimension, group homology and cohomology. If time permits, the instructor may choose to cover additional topics such as spectral sequences or Lie algebra homology and cohomology. Department enforced prerequisites: MATH 6130 and MATH 6140.
MATH 6360  Functions of a Complex Variable 2
Primary Instructor

Fall 2019
Focuses on conformal mapping, analytic continuation, singularities and elementary special functions. Department enforced prerequisite: MATH 6350. Instructor consent required for undergraduates.
MATH 8174  Topics in Algebra I
Primary Instructor

Spring 2022
Department enforced prerequisites: MATH 6130 and MATH 6140. Instructor consent required for undergraduates.