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Publications in VIVO

# Elliott, Peter D Professor

## Teaching

### courses taught

• MATH 3001 - Analysis 1
Primary Instructor - Fall 2019
Provides a rigorous treatment of the basic results from elementary Calculus. Topics include the topology of the real line, sequences of numbers, continuous functions, differentiable functions and the Riemann integral.
• MATH 3110 - Introduction to Theory of Numbers
Primary Instructor - Spring 2018
Studies the set of integers, focusing on divisibility, congruences, arithmetic functions, sums of squares, quadratic residues and reciprocity, and elementary results on distributions of primes.
• MATH 3510 - Introduction to Probability and Statistics
Primary Instructor - Spring 2019
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. Credit not granted for this course and MATH 2510 or MATH 4510.
• MATH 4510 - Introduction to Probability Theory
Primary Instructor - Fall 2018
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 4820 - History of Mathematical Ideas
Primary Instructor - Spring 2020
Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present. Recommended restriction: completion of upper division Written Communication requirement. Same as MATH 5820.
• MATH 5510 - Introduction to Probability Theory
Primary Instructor - Fall 2018
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 5820 - History of Mathematical Ideas
Primary Instructor - Spring 2020
Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present. Recommended requisite: completion of upper division Written Communication requirement. Same as MATH 4820.
• MATH 6190 - Analytic Number Theory
Primary Instructor - Spring 2020
Acquaints students with the Riemann Zeta-function and its meromorphic continuation, characters and Dirichlet series, Dirichlet's theorem on primes in arithmetic progressions, zero-free regions of the zeta function and the prime number theorem. Department enforced prerequisites: MATH 6110 and MATH 6350. Instructor consent required for undergraduates.
• MATH 6350 - Functions of a Complex Variable 1
Primary Instructor - Spring 2019
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 2018
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.

• Ph.D., 1965
• B.S., 1962