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### Mathematics (MA)

#### Department Website:

http://departments.juniata.edu/math/

#### Faculty:

- Professor John Bukowski (Chair) - ext. 3591
- Associate Professor Henry Escuadro - ext. 3596
- Professor Gerald Kruse - ext. 3595
- Associate Professor Kimberly Roth -ext. 3593
- Professor Catherine Stenson - ext. 3736
- Professor Benjamin Sunderland - ext. 3590
- Variety of mathematical software including Maple and Mathematica, the statistical packages Fathom, Minitab, and SPSS, and typesetting program LaTeX.
- Opportunity to attend occasional Mathematics Colloquium
- Opportunity to participate in events of Null Set (math club), including attendance at regional undergraduate mathematics conferences.
- Mathematics
- Mathematics and Secondary Education
- Mathematics and Physics
- Mathematics and Computer Science
- Biochemistry and Applied Mathematics
- Chemistry and Mathematics
- Mathematics and Finance
- French and Mathematics
- Requirements for a secondary emphasis in Mathematics are available and can be found at http://departments.juniata.edu/math/poes.html
- MASS program at Penn State University
- Summer Research experience for undergraduates at various universities
- 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 200-level 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 100-level mathematics with the QS designation.

#### 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.

#### Special programs, facilities, or equipment:

#### Programs of Emphasis:

#### Student Designed Programs of Emphasis:

#### Secondary Emphasis:

#### Internship/Research Experiences:

**Specific department policy:**

**Awarding credit for AP Exam scores:**

#### Courses:

*Many of the mathematics courses use mathematical software such as
Maple and statistics software such as Minitab to facilitate computation and
aid mathematical reasoning. *

MA-100 Precalculus (Fall & Spring; 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.

MA-103 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.

MA-116 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.

MA-130 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.

MA-155 The Heart of Mathematics (Spring; Yearly; 3.00 Credits; N) The goal of this course is to give non-mathematics students the hands-on experience of doing mathematics. Topics include infinity, higher dimensions, chaos, and probability. The emphasis will be on the process of doing mathematics: generating examples, looking for patterns, making conjectures, and proving these conjectures. May not be taken if you have completed MA130.

MA-160 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.

MA-199 Special Topics (Variable; Variable; 1.00-4.00 Credits) An introduction to one of the branches of mathematics not currently included in the regular course offerings.

MA-208 Symbolic Logic (Fall; Yearly; 3.00 Credits; N,H) See description for PL208.

MA-210 Foundations of Mathematics (Fall; Yearly; 3.00 Credits; CW) An introduction to the logical and set-theoretic 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 set-theoretic idiom. Prerequisites: MA160 or MA116 or PL208 or MA208 or permission of the instructor.

MA-220 Introduction to Probability & Statistics (Fall & Spring; Variable; 4.00 Credits; N,QS) 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.

MA-230 Calculus II (Fall & Spring; Yearly; 4.00 Credits; N,QM) Expands the treatment of two-space 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.

MA-233 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.

MA-235 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.

MA-299 Special Topics (Variable; Variable; 1.00-4.00 Credits) An introduction to one of the branches of mathematics not currently in the regular course offerings. Prerequisites: Vary depending on course offering.

MA-303 Mathematical Modeling (Fall; Yearly; 3.00 Credits; N,QM,CW) How to use mathematics to model " real-world " 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.

MA-316 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.

MA-320 Probability & Statistics (Spring; Even Years; 3.00 Credits; N,QS) Topics in mathematical statistics 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, chi-square, and normal distributions. Note: MA235 is recommended. Prerequisites: MA220 and MA230.

MA-325 Statistical Consulting (Variable; Variable; 2.00 Credits; N,QS,CW) The participating students will receive some training during the semester in consulting on statistical problems and will be expected to staff the Statistics Center and to assist in collaborative efforts with faculty and/or staff on projects. This provides the student with both real work experience in the field of statistics and a project based learning experience. May be taken multiple times for credit. Prerequisites: MA220 or BI305 or PY214 or EB211.

MA-335 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, MA230 and MA235 or MA233.

MA-340 Numerical Analysis (Spring; Even Years; 3.00 Credits; N,QM) Theory and application of numerical approximation techniques. Topics included are numerical error, root-finding, interpolation and polynomial approximation, numerical differentiation and integration, and differential equations. Prerequisites: MA160, MA130 and CS110 or permission. (Also listed as CS340.)

MA-350 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 non-Euclidean geometries. The roles of these discoveries in the history of mathematics are emphasized. Prerequisites: MA210 or PL208 or MA208.

MA-355 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.

MA-360 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.

MA-365 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.

MA-370 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.

MA-375 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.

MA-399 Special Topics (Variable; Variable; 1.00-4.00 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.

MA-480 Mathematics Seminar I (Fall; Yearly; 1.00 Credit; N) A discussion-based 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.

MA-481 Mathematics Seminar II (Fall; Yearly; 1.00 Credit; N) See MA480. Prerequisite: MA480.

MA-485 Mathematics Research (Fall & Spring; Yearly; 3.00-5.00 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.

MA-490 Mathematics Internship/Needs Paperwork (Fall & Spring; Yearly; 2.00-9.00 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.

MA-495 Internship Research/Seminar (Fall & Spring; Yearly; 2.00-6.00 Credits; N) Requires students to reflect on the internship experience and/or pursue research related to the placement. Corequisite: MA490. Prerequisite: permission.

MA-TUT Mathematics Teaching Assistant (Variable; Variable; 1.00-3.00 Credits; N)