Grant, David R

Research

research overview

Grant's research is in the area of number theory related to algebraic geometry, known as arithmetic geometry. He also applies this research to the construction of codes used for reliable digital communications. From time to time he is involved in mathematical education research into equitable mathematical education practices.

keywords

number theory, arithmetic geometry, coding theory

Publications

selected publications

chapter
- All-in University: Changing Everything at Once 2021
- Culture and Equity 2021
- Sustaining Active Learning 2021
- Space-time codes and non-associative division algebras arising from elliptic curves. Contemporary Mathematics. 29-44. 2008
- Theta functions and singular torsion on elliptic curves. 111-126. 2002
journal article
- Differential codes on higher dimensional varieties via Grothendieck's residue symbol. Journal of Pure and Applied Algebra. 2024
- On the universal p-adic sigma and Weierstrass zeta functions. Journal of Number Theory. 348-376. 2023
- Modeling human health behavior with a new index that measures connectivity. Preventive Medicine Reports. 102172-102172. 2023
- A higher-order generalization of Jacobi's derivative formula and its algebraic geometric analogue. Journal de Theorie des Nombres de Bordeaux. 361-386. 2021
- A generalization of Jacobi's derivative formula to dimension two, II. Acta Arithmetica. 403-420. 2019

Teaching

courses taught

MATH 2001 - Introduction to Discrete Mathematics
Primary Instructor - Fall 2021 / Spring 2023
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 Non-Mathematics Majors
Primary Instructor - Fall 2020 / Fall 2023 / Fall 2024
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 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 plan to major in Mathematics. Degree credit not granted for this course and MATH 2130 or APPM 3310. Formerly MATH 3135.
MATH 3140 - Abstract Algebra 1
Primary Instructor - Spring 2020
Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields.
MATH 3210 - Euclidean and Non-Euclidean Geometry
Primary Instructor - Spring 2021
Axiomatic systems; Euclid's presentation of the elements of geometry; Hilbert's axioms; neutral, Euclidean and non-Euclidean geometries and their models.

MATH 3430 - Ordinary Differential Equations
Primary Instructor - Fall 2022
Involves an elementary systematic introduction to first-order scalar differential equations, nth order linear differential equations, and n-dimensional linear systems of first-order differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness and numerical solutions. Formerly MATH 4430.

MATH 3450 - Introduction to Complex Variables
Primary Instructor - Spring 2018
Theory of functions of one complex variable, including integrals, power series, residues, conformal mapping, and special functions. Formerly MATH 4450.

MATH 3510 - Introduction to Probability and Statistics
Primary Instructor - Fall 2020 / Spring 2024
Introduces the basic notions of Probability: random variables, expectation, conditioning, and the standard distributions (Binomial, Poisson, Exponential, Normal). This course also covers the Law of Large Numbers and Central Limit Theorem as they apply to statistical questions: sampling from a random distribution, estimation, and hypothesis testing. Degree credit not granted for this course and MATH 2510 or MATH 4510.

MATH 4510 - Introduction to Probability Theory
Primary Instructor - Fall 2019
Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits. Degree credit not granted for this course and APPM 3570 or ECEN 3810 or MATH 3510. Same as MATH 5510.

MATH 5510 - Introduction to Probability Theory
Primary Instructor - Fall 2019
Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains if time permits. Same as MATH 4510.

MATH 6110 - Introduction to Number Theory
Primary Instructor - Fall 2019 / Fall 2022
Examines divisibility properties of integers, congruences, diophantine equations, arithmetic functions, quadratic residues, distribution of primes and algebraic number fields. Department enforced prerequisite: MATH 3140. Instructor consent required for undergraduates.

MATH 6350 - Functions of a Complex Variable 1
Primary Instructor - Spring 2024
Focuses on complex numbers and the complex plane. Includes Cauchy-Riemann equations, complex integration, Cauchy integral theory, infinite series and products, and residue theory. Department enforced prerequisite: MATH 4001. Instructor consent required for undergraduates.

MATH 8114 - Topics in Number Theory
Primary Instructor - Spring 2022
May include the theory of automorphic forms, elliptic curves, or any of a variety of advanced topics in analytic and algebraic number theory. Department enforced prerequisite: MATH 6110. Instructor consent required for undergraduates.

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Background

education and training

Ph.D., Massachusetts Institute of Technology 1985
B.A., Princeton University 1981

awards and honors

President's Teaching Scholar, conferred by University of Colorado President, 2018
BFA Award for Excellence in Teaching and Pedagogy, conferred by Boulder Faculty Assembly, 1991

VIVO

Positions

Research Areas

Research

research overview

keywords

Publications

selected publications

chapter

journal article

Teaching

courses taught

Background

education and training

awards and honors

International Activities

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