Department Website:
https://www.juniata.edu/academics/departments/mathematics/
Faculty:
 Professor John Bukowski  ext. 3591
 Associate Professor Kristin Camenga  ext. 3590
 Professor Henry Escuadro (Chair)  ext. 3596
 Assistant Professor Melissa Innerst  ext. 4134
 Professor Gerald Kruse (Dale Professor)  ext. 3595
 Professor Kimberly Roth  ext. 3593
 Professor Catherine Stenson  ext. 3736
Background Information:
Mathematics is arguably the most fundamental of all academic disciplines. Often called the universal language, mathematics underlies a great part of the physical sciences and also has important connections to computer science, philosophy, economics and business, music, and many other fields. At the same time, mathematics can be regarded as high art, well worth studying for its stark beauty alone. Contrary to beliefs that it is a static discipline, mathematics is currently in a period of explosive growth in its internal development and its applications, and in the use of technology to enhance and extend our understanding. At Juniata, we strive to equip our students to appreciate and participate in this exciting evolution. To this end, we are fortunate to enjoy close ties with the departments of Information Technology and Computer Science, Physics, and Accounting, Business, and Economics. Just as important, we have a close working relationship with the Education Department to support a strong preparation for teaching mathematics at the secondary level.
The mathematics department also offers courses in statistics. Statistics is the science of collecting, organizing, analyzing and presenting data. Math faculty teach courses in statistics within the department and as part of the Data Science Program.
Special programs, facilities, or equipment:
 Mathematical software: includes Maple, the statistical packages R and StatKey, and the typesetting program LaTeX.
 Mathematics Colloquium: hourlong talks several times a semester from faculty and professionals who use mathematics and statistics.
 Null Set: our studentled math club organizes events including Pi Day Celebration, Math Jeopardy, and attendance at regional undergraduate mathematics conferences.
 Pi Mu Epsilon: qualified students can be nominated to the Juniata Chapter of this national honors society.
 Distinction: exceptionally strong students are invited to pursue Distinction in their Program of Emphasis.
Programs of Emphasis:
 Mathematics
 Mathematics and Secondary Education
 Data Science
Individualized Programs of Emphasis:
 Mathematics and Physics
 Mathematics and Computer Science
 Biochemistry and Applied Mathematics
 Chemistry and Mathematics
 Mathematics and Finance
 French and Mathematics
Secondary Emphasis:
 Mathematics
 Data Science
Internship/Research Experiences:
 Internships both for credit and for transcript notation are available to Juniata Students. Recent internships include the Office of Institutional Research, Mutual Benefit Corporation, and Excela Health.
 Students have the opportunity to pursue undergraduate research in mathematics or statistics with Juniata faculty.
 Students can engage in summer research with peers from other colleges through the Research Experience for Undergraduate programs of other institutions.
 Students considering graduate studies in mathematics can participate in the Mathematics Advanced Study Semesters program at Penn State University.
Study Abroad Opportunities:

The Budapest Semesters in Mathematics and Mathematics Education (Budapest, Hungary) and the Mathematical Sciences Semester (Guanajato, Mexico) are programs that cater to students who wish to take mathematics courses while studying abroad.
Specific department policy:
Awarding credit for AP Exam scores:
 for a score of 4 or 5 on the Calculus AB exam. If the student accepts the AP credit, he/she may then schedule Calculus II if so desired, but may NOT take Calculus I for (additional) credit.
 for a score of 4 or 5 on the Calculus BC exam. We award credit for Calculus I, plus two additional credits of general 200level mathematics. If the student accepts the AP credit, he/she may then schedule Calculus II if so desired, but may NOT take Calculus I for (additional) credit.
 for a score of 4 or 5 on the Statistics exam. We award three credits of general 100level mathematics with the QS designation.
Courses:
Many of the mathematics courses use mathematical software to facilitate computation and aid mathematical reasoning.
MA100 Precalculus (Fall; Yearly; 3.00 Credits; N,QM) This course is designed for students who need a structured review of precalculus mathematics. Topics covered include solving equations and inequalities, graphing, and analysis of functions, including polynomial and rational functions, exponential and logarithmic functions and trigonometric functions. Integrates the use of the software package Maple in classroom demonstrations and homework assignments. This course cannot be included in a mathematics POE. Prerequisites: High school algebra and trigonometry.
MA103 Quantitative Methods (Fall & Spring; Yearly; 3.00 Credits; Q) This course prepares students to be quantitatively literate citizens in today's world. By learning to think critically about quantitative issues, students will be able to make responsible decisions in their daily lives. Problems are analyzed and solved using numerical, graphical, statistical, and algebraic reasoning. Technology is used to help visualize data and facilitate calculations, as well as to present quantitative output and verbal arguments.
MA109 Mathematical Problem Solving (Variable; Yearly; 3.00 Credits; QM,WKFR) In this course, students use unsophisticated math to find solutions to problems. Many of the math concepts will be familiar but there are some that will be new. The focus will be on using math creatively to answer questions of interest. Unlike standard math exercises that ask students to apply techniques to come up with a numerical answer or an expression, the questions require students to use the mathematics they know to come up with a strategy to accomplish a task or make meaningful decisions. Prereq or Coreq: FYC101 or EN110 or EN109.
MA116 Discrete Structures (Fall; Yearly; 4.00 Credits; N,Q) Introduces mathematical structures and concepts such as functions, relations, logic, induction, counting, and graph theory. Their application to Computer Science is emphasized. Prerequisite high school algebra.
MA130 Calculus I (Fall & Spring; Yearly; 4.00 Credits; N,QM) An introduction to calculus including differentiation and integration of elementary functions of a single variable, limits, tangents, rates of change, maxima and minima, area, volume, and other applications. Integrates the use of computer algebra systems, and graphical, algebraic and numerical thinking.
MA138 Mathematics and Democracy (Variable; Yearly; 4.00 Credits; N,QM,WKFR) Introduction to topics in mathematics related to democracy including voting theory, gerrymandering, and apportionment. We will discuss the comparison between these topics mathematically versus politically. Prerequsite or Corequisite: FYC101 or EN110 or EN109.
MA155 The Heart of Mathematics (Spring; Yearly; 3.00 Credits; N,WKFR) The goal of this course is to give a broad range of students the handson experience of doing mathematics. Topics may include infinity, higher dimensions, chaos, and graph theory. The emphasis will be on the process of doing mathematics: generating examples, looking for patterns, making conjectures, and proving these conjectures. Prerequisites: FYC 101.
MA160 Linear Algebra (Fall & Spring; Variable; 3.00 Credits; N,QM) An introduction to systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues, and applications.Prerequisites: MA130.
MA199 Special Topics (Variable; Variable; 1.004.00 Credits) An introduction to one of the branches of mathematics not currently included in the regular course offerings.
MA205 Elementary Statistics (Variable; Yearly; 4.00 Credits; N,QS,WKSP) Introduction to traditional statistical concepts including descriptive statistics, binomial and normal probability models, confidence intervals, tests of hypotheses, linear correlation and regression, twoway contingency tables, and oneway analysis of variance. PreReq or CoReq: FYC101 or EN110 or EN109.
MA208 Symbolic Logic (Variable; Yearly; 4.00 Credits; N,H,WKFR) An introduction to the basics of firstorder logic: the concept of artificial language, techniques for symbolizing ordinary languages and arguments, formal inference systems (either truth free method or natural deduction), and other advanced topics in firstorder logic. It has no prerequisites beyond high school algebra.
MA210 Foundations of Mathematics (Fall; Yearly; 3.00 Credits; CW) An introduction to the logical and settheoretic basis of modern mathematics. Topics covered include propositional and predicate logic; induction; naive and axiomatic set theory, binary relations, mappings, infinite sets and cardinality; finite sets and combinatorics; and an introduction to the theory of computability. Students will learn to read and to express mathematical ideas in the settheoretic idiom. Prerequisites: MA160 or MA116 or PL208 or MA208 or permission of the instructor.
MA220 Introduction to Probability & Statistics (Fall & Spring; Variable; 4.00 Credits; N,QS,CTGES) An introduction to the basic ideas and techniques of probability theory and to selected topics in statistics, such as sampling theory, confidence intervals, and linear regression. Prerequisite: MA130.
MA230 Calculus II (Fall & Spring; Yearly; 4.00 Credits; N,QM) Expands the treatment of twospace using polar and parametric equations. Emphasizes multivariable calculus, including vectors in three dimensions, curves and surfaces in space, functions of several variables, partial differentiation, multiple integration, and applications. Prerequisite: MA130.
MA233 Integrals Series & Differential Equations (Fall; Yearly; 2.00 Credits; N) Integration, Taylor and Fourier series, and an introduction to differential equations, with applications and the use of the software package Maple. (Course meets four times per week and concludes at midterm.) Note: A student may receive credit for MA233 or MA235, but not for both. Prerequisite: MA130.
MA235 Calculus III (Fall; Yearly; 4.00 Credits; N,QM) A continuation of the calculus sequence. Topics include methods of integration by Simpson's Rule, applications, Taylor and Fourier series; introduction to ordinary differential equations; integration in polar, cylindrical, and spherical coordinates; differential and integral vector calculus. Prerequisites: MA230.
MA299 Special Topics (Variable; Variable; 1.004.00 Credits) An introduction to one of the branches of mathematics not currently in the regular course offerings. Prerequisites: Vary depending on course offering.
MA303 Mathematical Modeling (Fall; Yearly; 3.00 Credits; N,QM,CW) How to use mathematics to model " realworld " problems. Modeling topics range from population dynamics to economics to the nuclear arms race. Mathematical tools range from calculus to curve fitting to computer simulation. How to make a little bit of mathematics go a long way. Note: MA160 is recommended. Prerequisite: MA130 and experience with programming and Minitab.
MA316 Combinatorics (Fall; Even Years; 3.00 Credits; QM,N) Advanced counting: what they didn't teach you on Sesame Street. An introduction to graphs, trees, and enumeration techniques with applications to computer science and biology. Prerequisites: MA116 or MA210 or MA220 or permission of the instructor.
MA321 Multivariate Statistics (Spring; Variable; 3.00 Credits; N,QS) A class in multivariate statistical techniques including nonparametric methods, multiple regression, logistic regression, multiple testing, principle analysis. Prerequisites: An introductory statistics course ( MA220 or BI305 or PY214 or EB211) and linear algebra (MA 160) or Calculus 1 (MA 130).
MA322 Probability (Spring; Even Years; 3.00 Credits; N,QM) Topics in probability including discrete and continuous random variables, expectations, mean, variance, moment generating functions, multivariate distributions, correlation, and independence, all leading to an efficient study of the binomial, Poisson, gamma, chisquare, and normal distributions. Prerequisites: MA220 and MA230; MA235 is recommended.
MA325 Statistical Consulting (Variable; Yearly; 3.00 Credits; N,QS,CW,SWLE) The participating students will receive training during the semester in consulting on statistical problems and to assist in collaborative efforts with faculty and/or staff on clientpartnered projects that are predetermined. The semesterlong project provides the student with both real work experience in the field of statistics and a projectbased learning experience in partnership with the client. May be taken multiple times for credit. PreReqs: FYC101 or EN110 or EN109; any one course from the following list: BI305, EB211, ESS230, ESS309, MA205, MA220, PY361, or SW215.
MA335 Differential Equations (Spring; Yearly; 4.00 Credits; N,QM) Theory and application of ordinary differential equations. Emphasis on modern qualitative techniques, with numerical and analytical approaches used when appropriate. Contains a brief introduction to partial differential equations. Prerequisites: MA130 and MA230 and MA235 or MA233.
MA340 Numerical Analysis (Spring; Even Years; 3.00 Credits; N,QM) Theory and application of numerical approximation techniques. Topics included are numerical error, rootfinding, interpolation and polynomial approximation, numerical differentiation and integration, and differential equations. Prerequisites: MA160, MA130 and CS110 or permission. (Also listed as CS340.)
MA341 Scientific Computing (Variable; Yearly; 3.00 Credits; N) This course begins with an introduction to fundamental concepts in Scientific Computing and concludes with domainspecific projects in areas like Bioinformatics, Data Science, Physical Systems, and Numerical Analysis. The common content will include commandline interfaces (Linux), programming languages (Jupyter/Python), numerical and graphical libraries (NumPy and Matplotlib), versioncontrol (Git/Github), and relational databases (SQL). PreReq: CS110.
MA350 Topics in Geometry (Spring; Odd Years; 3.00 Credits; N) Examines the history and development of geometry with an axiomatic development of Euclidean geometry leading to an investigation of hyperbolic and elliptical nonEuclidean geometries. The roles of these discoveries in the history of mathematics are emphasized. Prerequisites: MA210 or PL208 or MA208.
MA355 Nature of Mathematics (Spring; Odd Years; 1.00 Credit) An introduction to the history and philosophy of mathematics. Briefly traces the historical development of mathematics from its Oriental and Greek origins to modern times. Surveys the different philosophies of mathematics and provides some insight into the current crisis in the foundations of mathematics. Corequisite: MA350. Prerequisite: MA210 or PL208 or MA208.
MA360 Abstract Algebra (Spring; Even Years; 3.00 Credits) Investigates the algebraic properties of the real numbers and their generalizations. Emphasis on group theory, with introductions to integral domains, rings, fields and vector spaces. Prerequisites: MA160 and MA210.
MA365 Number Theory (Fall; Odd Years; 3.00 Credits; N) An investigation of topics in Elementary Number Theory including divisibility, primes, congruence, congruence equations, quadratic residues and quadratic reciprocity, arithmetic and multiplicative functions, Diophantine equations, and other topics selected according to interest. Prerequisites: MA210 or permission of the instructor.
MA370 Real Analysis (Spring; Odd Years; 3.00 Credits; N) Focuses on functions of a real variable, sequences, limits, continuity, differentiation and the derivation of standard theorems of the differential calculus. Prerequisites: MA210 and MA230 and MA235.
MA375 Complex Analysis (Fall; Even Years; 3.00 Credits; N) Algebra and geometry of the complex numbers, analytic functions, complex integration, Taylor and Laurent series, residue theory, physical applications, and other topics as time allows. Prerequisites: MA235.
MA399 Special Topics (Variable; Variable; 1.004.00 Credits) An introduction to one of the branches of mathematics not currently included in the regular course offerings, such as number theory, history of mathematics, chaos and fractals, topology, graph theory, mathematical logic. Prerequisites: Vary depending on course offering. Note: abbreviated ST: Students may take each ST: course for credit.
MA480 Mathematics Seminar I (Fall; Yearly; 1.00 Credit; N) A discussionbased study of current mathematical literature and modeling problems. Students will both apply their previous mathematical knowledge and explore new topics. In addition, students may use this course as preparation for an individual research project to be completed in MA485. A junior taking this course may repeat it as a senior as MA481. Prerequisites: junior or senior standing, MA160, MA210 and MA235 or permission of the instructor.
MA481 Mathematics Seminar II (Fall; Yearly; 1.00 Credit; N) See MA480. Prerequisite: MA480.
MA485 Mathematics Research (Fall & Spring; Yearly; 3.005.00 Credits; N) Allows students to pursue a program of directed original research in pure or applied mathematics. Required of candidates for distinction in mathematics POE. Prerequisites: MA480.
MA490 Mathematics Internship/Needs Paperwork (Fall & Spring; Yearly; 2.009.00 Credits; N) Placement with an organization applying mathematical techniques such as statistical analysis, operations research, actuarial mathematics, or systems analysis. Designed to afford the student an opportunity to apply analytical and technical skills developed in the POE. Prerequisites: POE in Mathematics, permission and Jr. or Sr. Standing. Corequisite: MA495.
MA495 Internship Research/Seminar (Fall & Spring; Yearly; 2.006.00 Credits; N) Requires students to reflect on the internship experience and/or pursue research related to the placement. Corequisite: MA490. Prerequisite: permission.
MATUT Mathematics Teaching Assistant (Variable; Variable; 1.003.00 Credits; N)