Mathematics

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The Math department congratulates Math major and Economics minor Mica Hanish ’21, who was named NCAC Student-Athlete of the Week. As noted in the announcement:

Hanish, a mathematics major with a 4.00 cumulative GPA, was named a CoSIDA Academic All-America first-team selection last season, only the third individual in Allegheny women’s track & field and cross country history to earn that honor. She is also a distinguished Allegheny Alden Scholar (GPA above 3.80) and is a member of Chi Alpha Sigma, the national student-athlete honor society, and Pi Mu Epsilon, the national mathematics honor society, where she serves as treasurer of Allegheny’s chapter. In her cross country career, Hanish has garnered All-NCAC selections three times, including two first-team honors and one second-team honor, while also earning three All-Region honors. On the track, she has earned All-NCAC accolades in the 3000-meter run, DMR, one-mile and 5000-meter run. In March, she was named All-Region for her performances in the mile and 3,000-meter run.

The faculty and staff of the Mathematics department congratulate Math major Ryan Clydesdale and Math minor Olivia Krieger on being named co-valedictorians of the class of 2020. Ryan and Olivia, although we weren’t able to celebrate you in person this year, we are very proud of your achievements.

Ryan Clydesdale, a Math major with a double minor in Chemistry and Economics, was also awarded the Frederick H. Steen Prize for Excellence in Mathematics and was a previous recipient of a Cornerstone Research summer internship. A member of the men’s soccer team, Ryan also received the William Crawford Academic Merit Award in Athletics – Male, recognizing him as the male scholar-athlete with the highest grade-point average.

Olivia Krieger, a Physics major with a double minor in Mathematics and Philosophy, was also awarded the Richard L. Brown Physics Prize. Olivia presented her research at the 2019 Conference for Undergraduate Women in Physics, where she also won best poster in her category.

Will Crosby `21, Mica Hanish `21, and Megan Powell `21, students in Professor Tamara Lakins’ spring 2020 Mathematics Junior Seminar, chose the May 2020 winner of The College Mathematics Journal Next Generation Prize.  The prize was awarded to the journal article in the May 2020 issue that the students selected as the best for undergraduate mathematics students nationwide to read.  The prize was created to promote undergraduate students’ reading of The College Mathematics Journal (published by the Mathematical Association of America), and to encourage the writing of expository mathematics that is student-accessible.  The Allegheny College students were thanked in the May 2020 issue.

MATH 205 – Foundations of Mathematics
Instructor: Professor Lakins
An introduction to concepts encountered in the study of abstract mathematics. Topics covered include logic, mathematical proofs, set theory, relations, functions, mathematical induction, and introductory number theory. The concepts of injectivity, subjectivity, and inverses are discussed as well as elementary computational tools such as the Division Algorithm and Euclid’s algorithm for the greatest common divisor. Additional topics may include cardinality, combinatorics, graph theory, algebraic structure, the real number system, and concepts of mathematical analysis.
Prerequisite: MATH 152 or MATH 160 with a grade of C or better.
Distribution Requirements: ME, SP.

MATH 211 – Vector Calculus and Several Variable Integration
Instructor: Professor Carswell
A study of integration of functions of several variables, including the use of polar, cylindrical, and spherical coordinate systems; and vector calculus, including vector fields, line and surface integrals, and the theorems of Green and Stokes.
Prerequisite: MATH 152 with a grade of C or better.
Distribution Requirements: QR.
May not be taken for credit if a grade of C or better in MATH 210 has already been received.

MATH 270 – Optimization and Approximation
Instructor: Professor Ellers
A study of optimization of functions of one variable and of several variables, including the Extreme Value Theorem and Lagrange multipliers; sequences and series; and Taylor approximation of functions.
Prerequisite: MATH 152 with a grade of C or better.
Distribution Requirements: QR.
May not be taken for credit if a grade of C or better in MATH 170 has already been received.

MATH 280 – Ordinary Differential Equations
Instructor: Professor Carswell
An examination of methods of solving ordinary differential equations with emphasis on the existence and uniqueness of solutions of first order equations and second order linear equations. Topics may include Laplace transforms, systems of linear differential equations, power series solutions, successive approximations, linear differential equations, and oscillation theory with applications to chemistry and physics.
Prerequisite: MATH 152 or MATH 210 with a grade of C or better.
Distribution Requirements: SP.

MATH 325 – Algebraic Structures I
Instructor: Professor Werner
An introduction to the notion of an algebraic structure concentrating on the simplest such structure, that of a group. Rings and fields are also discussed.
Prerequisite: MATH 205 and MATH 320, each with a grade of C or better.
Distribution Requirements: SP.

MATH 340 – Introduction to Analysis
Instructor: Professor Weir
An examination of the theory of calculus of a single variable. Topics include properties of the real numbers, topology of the real line, and a rigorous treatment of sequences, functions, limits, continuity, differentiation and integration.
Prerequisite:  MATH 205 with a grade of C or better, and a grade of C or better in one of the following courses: MATH 210, MATH 211, MATH 270, MATH 280.
Distribution Requirements: SP.

MATH 345 – Probability and Statistical Inference I
Instructor: Professor Lo Bello
A study of mathematical models, sample space probabilities, random variables, expectation, empirical and theoretical frequency distributions, moment generating functions, sampling theory, correlation and regression.
Prerequisite: MATH 152 or MATH 210 with a grade of C or better.
Distribution Requirements: SP.
This is one of the possible mathematics courses that may be substituted for one of the required 300-level CMPSC courses in the Computer Science major.

MATH 370 – Graph Theory and Combinatorics **New Course**
Instructor: Professor Dodge
A study of finite graphs and combinatorics, covering enumeration of combinatorial structures, directed and undirected graphs, and recursive algorithms. Topics include trees, planarity, graph coloring, Eulerian and Hamiltonian graphs, shortest path algorithms, the pigeonhole principle, permutations and combinations of finite sets and multisets, binomial and multinomial coefficients, and the inclusion-exclusion principle.
Prerequisites: MATH 205 with a grade of C or better
Distribution Requirements: SP
This is one of the mathematics courses that may be substituted for one of the required 300-level CMPSC courses in the Computer Science major.