Dr. Manley's research is primarily directed at the intersection of the theory of integral transforms, functional analysis, and mathematical physics, that being the generalizations of the Fourier transform.
keywords
generalizations of the fourier transform, special functions, mathematical physics
Teaching
courses taught
MATH 1112  Mathematical Analysis in Business
Primary Instructor

Spring 2020
Gives students experience with mathematical problem solving in real business contexts. Students will work with data and spreadsheets to build and analyze mathematical models. Themes of the course include applying logical operators to model business rules, interpreting data and using tables and graphs, finding breakeven and optimal points, and addressing uncertainty and forecasting Degree credit not granted for this course and MATH 1012.
MATH 1150  Precalculus Mathematics
Primary Instructor

Fall 2018 / Spring 2019 / Fall 2019 / Spring 2020 / Fall 2020 / Spring 2021 / Fall 2021 / Spring 2022 / Fall 2022 / Spring 2023 / Fall 2023
Develops techniques and concepts prerequisite to calculus through the study of trigonometric, exponential, logarithmic, polynomial and other functions. For more information about the math placement referred to in the "Enrollment Requirements", please contact your academic advisor. Degree credit not granted for this course and APPM 1235 or MATH 1021.
MATH 2001  Introduction to Discrete Mathematics
Primary Instructor

Summer 2018 / Spring 2019 / Summer 2019 / Summer 2020 / Summer 2021 / 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 2002  Number Systems: An Introduction to Higher Mathematics
Primary Instructor

Fall 2023
Introduces the concepts of mathematical proofs using the construction of the real numbers from set theory. Topics include basic logic and set theory, equivalence relations and functions, Peano's axioms, construction of the integers, the rational numbers and axiomatic treatment of the real numbers. Credit not granted for this course and MATH 2001.
MATH 2130  Introduction to Linear Algebra for NonMathematics Majors
Primary Instructor

Spring 2018 / Fall 2019 / Spring 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 do not plan to major in Mathematics. Degree credit not granted for this course and MATH 2135 or APPM 3310. Formerly MATH 3130.
MATH 2300  Calculus 2
Primary Instructor

Spring 2018 / Spring 2019 / Summer 2019 / Fall 2023 / Spring 2024
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 2400  Calculus 3
Primary Instructor

Fall 2018 / Spring 2024
Continuation of MATH 2300. Topics include vectors, threedimensional analytic geometry, partial differentiation and multiple integrals, and vector analysis. Department enforced prerequisite: MATH 2300 or APPM 1360 (minimum grade C). Degree credit not granted for this course and APPM 2350.
MATH 2510  Introduction to Statistics
Primary Instructor

Summer 2018
Elementary statistical measures. Introduces statistical distributions, statistical inference, hypothesis testing and linear regression. Department enforced prerequisite: two years of high school algebra.
MATH 3510  Introduction to Probability and Statistics
Primary Instructor

Spring 2022
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 3850  Seminar in Guided Mathematics Instruction
Primary Instructor

Fall 2018 / Spring 2019 / Fall 2019 / Spring 2020 / Fall 2020 / Spring 2021 / Fall 2021 / Spring 2022 / Fall 2022 / Spring 2023
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.