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Mathematics
 

Professor Daniel Falabella, Ph.D. , Chair
Associate Professors
Christopher J Catone, Ph.D. and David B. Nawrocki, Ph.D. '87
Assistant Professor Brittany Shelton, Ph.D.
Professors Emeritus Arthur Hilt, Ph.D. '54 and Raymond J. Mest '62


Developing the Problem-Solving Skills Valued in a Technologically Advanced Society

From the design of computers, logistics of airline scheduling, the creation of more efficient engines, to the pricing of commodities made by corporations, mathematics is the language of business and the sciences. Mathematics majors at Albright College master the problem-solving and analytical skills that are instrumental and highly valued in our society.  The mathematics curriculum is designed to offer a good balance between applied and theoretical mathematics.  Faculty members also employ the latest technology combined with traditional and experiential learning techniques to optimize the learning environment in the classroom.

The Mathematics Department offers a bachelor of science degree (B.S.) in mathematics. Courses are designed to provide a thorough undergraduate training in mathematics for students who wish to pursue graduate study, teach mathematics in secondary or elementary schools, or work in various fields in business, science and industry.

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Innovative Teaching and Individualized Attention

Students in both upper and lower level mathematics courses receive highly individualized attention from faculty members. Approximate class sizes are:

  • Freshman calculus sequence: 15-25 students
  • Sophomore classes: 8-15 students
  • Junior and senior classes: 5-12 students

These small class sizes allow faculty members to easily and effectively address student needs both inside and outside the classroom.

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Current Technology

While our students are well versed in theoretical mathematics, we also feel that it is important for our students to know when and how to apply current technology to solve complex problems. For this reason, professors in the mathematics department use a wide array of technology in the classroom. Technology currently employed by our faculty members includes graphing calculators; such as, the TI-89 and TI-200; Matlab; and Excel with Visual Basic Programming. Each of these technologies is used extensively in fields of education and business.

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Success After Graduation

Wondering what you can do with a major in mathematics?

You will find the diversity of positions held by mathematics majors graduating from Albright College to be both surprising and encouraging. Some of the companies graduates have worked for include:

  • Metropolitan Edison
  • AT&T
  • Wagner Engineering
  • I.B.M.
  • Aetna Life Insurance
  • Lockheed Martin

Graduate/professional school opportunities include law school, engineering school, and medical school, depending upon your interests and background.

In our technology-driven economy, the skills developed by our mathematics majors (quantitative-reasoning, problem-solving, communication, etc.) are becoming highly valued across many different fields. To give you a better feel for this diversity, we have listed below a few positions held by Albright College mathematics majors along with their earned degrees.

  • Data Processing Manager, Intersearch, Math
  • Accountant, Glen Gery, Math/Accounting
  • Teacher, Muhlenberg High School , Math
  • Life Actuary, Math/Economics
  • Engineering Group Leader, Litton Electronic Devices, Math/Physics
  • Statistician, Department of Labor & Industry, Math/Economics
  • Systems Engineer, AT&T, Math/Physics
  • Senior Software Engineer, Fidelity Investments, Math/Physics
  • General Manager, Systems & Computer Technology, Math/CSC
  • Medical Stop Loss Underwriter, American Insurance Managers, Math/Economics
  • QA Analyst, Wiesberger, Math
  • Research Scientist, East Penn Manufacturing, Math/Physics
  • Editor, Learning Design Associates, Math
  • Finance Supervisor, Interspace Airport Advertising, Math
  • Programmer, Lockheed Martin, Math/Economics
  • Computer Specialist, G.E. Richards Graphics Supplies, Math
  • Operations Research Analyst, US Army, Math
  • Research Engineer, Bethlehem Steel, Math/Physics

For more information about jobs for mathematics majors, visit the following web sites:

http://www.ams.org/employment/undergrad.html
http://www.maa.org/students/career.html
http://www.amstat.org/careers/index.cfm
http://www.beanactuary.org

Other resources available on campus are:

  • Great Jobs for Math Majors, Lambert & DeCotis (held in the Career Development Center)
  • 101 Careers in Mathematics, Sterrett (held in the library)

If you are unsure of the type of career direction you would like to take, you may want to consider a summer internship. This is a great way to get some work-related experience and explore any professions of interest to you. The Career Development Center has a listing of companies that offer summer internships.

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Major in Mathematics

Requirements:

  • MAT 131, 132 (MAT 131 satisfies the general studies quantitative reasoning requirement)
  • MAT 233
  • MAT 250, 320, 325 or 440, 431
  • MAT 491 and 492
  • Four elective mathematics courses at the 300-400 level to be chosen with departmental approval.
  • PHY 201 (satisfies the general studies natural science requirement)

Students interested in pursuing graduate study in mathematics are strongly encouraged to take MAT 310, 320, 325, 334, 360, 435, 438 and 440.

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Secondary Education Certification in Mathematics

The mathematics education program provides a sound foundation in mathematics combined with secondary education courses. Graduates of the program will be certified for secondary teaching in mathematics, meeting all Pennsylvania state requirements for certification.

Students interested in teacher certification in mathematics should consult Education Department faculty for specific requirements to meet both college and state guidelines.

Requirements:

  • MAT 131, 132 (MAT 131 satisfies the general studies quantitative reasoning requirement)
  • MAT 233
  • MAT 250, 310, 320, 325, 334 or 360, 340, 431 
  • MAT 491, 492
  • PHY 201 (satisfies the general studies natural science requirement)
  • PHI 202 (PHI 202 satisfies either the general studies-humanities or general studies interdisciplinary requirement)

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Combined Major in Mathematics

Requirements:

  • MAT 131 (satisfies general studies quantitative reasoning requirement)
  • MAT 132
  • MAT 233
  • MAT 250
  • MAT 492
  • Three elective mathematics courses at the 300-400 level, excluding MAT 491.  MAT 491 may be used to partially satisfy this requirement with departmental approval.

Note: MAT 102, 103, 104, 110, 120 and 125 do not satisfy any degree requirements for the mathematics major or combined major.

Please note that, at the discretion of the individual instructor, the TI-89 graphing calculator may be used in certain courses. For these courses it is highly recommended that the student purchase a TI-89 (or the comparable TI-200) graphing calculator. For more information, please contact your instructor.

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COURSES

MAT 102
Topics in Mathematics
This course provides a general survey of mathematical topics that are useful in a variety of fields.  Topics include: set theory and logical operators; topics in number theory including graph theory, Euler circuits, Hamiltonian circuits, and search algorithms; voting methods; and topics in interest rate theory.

MAT 103
Discrete Mathematics I

This is an introduction to the theory and application of discrete mathematics. Topics include logic, sets, functions and relations, combinations and elementary probability.

MAT 104
Discrete Mathematics II

A continuation of MAT 103, this course includes trees and graphs, recurrence relations, elementary group theory and selected topics in computer science.

MAT 110
Elementary Statistics

This course gives students a general overview of modern statistics. Topics include: organization of data; probability and probability distributions; measures of central tendency and variability; normal distributions; sampling; hypothesis testing; correlation and regression. A TI-89 graphing calculator is highly recommended.

MAT 120
Pre-Calculus Mathematics

This is a review of algebra and trigonometry intended to be taken before 131 or 125 by those students whose background in algebra and trigonometry is insufficient. The major emphasis is on the function concept. Elementary analytic geometry is discussed, along with algebra, composition of functions, inverse functions, trigonometry, and logarithmic and exponential functions.

MAT 125
Calculus with Business/Economics Applications

Designed as a one-semester course for concentrators in business administration or economics, topics such as linear functions and models; matrices and matrix algebra; linear systems; functions and graphs; derivatives and integrals; and extremization are included. Partial differentiation also is introduced.

MAT 131
Calculus and Analytic Geometry I

This course involves fundamental concepts of functions of one variable. Topics include: limits, continuity differentiation, derivative applications, curve sketching, related rates and maxima-minima problems. Introduction to indefinite and definite integration including the fundamental theorems, and numeric approximation techniques are also covered. This is normally the first mathematics course taken by students entering a math or math-related curriculum.

MAT 132
Calculus and Analytic Geometry II

A continuation of MAT 131. Topics include transcendental functions, applications of integration including volume, surface area, arc length and work.  Also covered are integration techniques, indeterminate forms, improper integrals, sequences and series, and Taylor’s theorem.
Prerequisite: MAT 131

MAT 233
Calculus III

A continuation of MAT 132. Topics include polar coordinates, parametric representation, vectors, analysis of functions of two (or more) variables, multiple integration, line and surface integrals. Normally taken by mathematics concentrators in the first semester of the sophomore year.
Prerequisite: MAT 132

MAT 250
Foundation of Mathematics

This is an introduction to abstract mathematics. Topics include symbolic logic, methods of proof (direct, contradiction and induction), set theory, relations, functions, countable and uncountable sets. Normally taken by mathematics concentrators in the first semester of the sophomore year.
Prerequisite: MAT 132 or permission of the department

MAT 310
Probability and Mathematical Statistics

This course introduces probability and mathematical statistics at the level presupposing knowledge of calculus. Descriptive and inferential statistics are included, along with hypothesis testing, estimation and analysis of variance.
Prerequisite: 132 & 250 or permission of the department

MAT 320
Linear Algebra

This is an introduction to matrix algebra; linear equations; linear dependence; determinants; vector spaces; linear transformations, eigenvalues, eigenvectors and diagonalization.
Prerequisites: MAT 132 & 250 or permission of the department

MAT 325
Abstract Algebra

This is an introduction to groups, rings and fields with topics selected from number theory, ideals and polynomial rings.
Prerequisite: MAT 250 or permission of the department

MAT 334
Differential Equations

This course is a study of solution techniques for ordinary differential equations. Topics include the principal types of equations of first and second order, linear equations with constant coefficient, higher order linear and non-linear equations, series solutions, operational methods, systems of equations and modeling problems. Runge- Kutta and other numerical approximation methods are also covered.
Prerequisite: MAT 233 & 320 or permission of the department

MAT 340
Geometry

This course is intended primarily for those students planning to enter the field of secondary education. It begins with a study of the most important ideas of Euclidean plane geometry, but also considers the historical significance of Euclid's original postulates. Special attention is given to the notion of parallelism of lines and the resulting non-Euclidean geometries when the axiom of parallelism is altered. Differential geometry also is introduced as a means of studying curves, surfaces and curves on surfaces.
Prerequisites: MAT 233 & 250 or permission of the department

MAT 360
Numerical Analysis

This is a study of numerical methods used in interpolation, differentiation and integration, solutions of equations and systems of equations, solutions of differential equations, fitting of empirical data and error estimation.  Some computer or calculator programming will be employed and a basic level of programming is assumed.  Applications are made to the sciences and engineering.
Prerequisite: MAT 233 & 250 or permission of the department

MAT 431
Real Analysis

This course is designed to take a rigorous look at definitions, theorems and concepts taken from the foundational calculus courses. Rigorous treatment is given to topics such as continuity, mean-value theorems, analysis of functions of several variables, extremization and limits. Other topics include sequences, series, the Heine-Borel covering theorem and the Riemann Integral.
Prerequisites: MAT 233 & 250 or permission of the department

MAT 435
Partial Differential Equations

Topics include: Orthogonal functions; Sturm-Liouville system; initial and boundary value problems; Fourier series; higher transcendental functions; separation-of-variables method; and other methods of solution of equations of mathematical physics.
Prerequisite: MAT 233, 250 & 334 or permission of the department

MAT 438
Complex Analysis

This is an introduction to the theory of functions of complex variables: derivatives and integrals; Cauchy's theorem; power series; theory of residues; and conformal mappings.
Prerequisite: MAT 233 & 250 or permission of the department

MAT 440
Introduction to Topology

This course introduces definitions and properties of topological spaces, metric spaces, continuity, homeomorphisms, separation axioms, compactness, connectedness, and fundamental group.
Prerequisites: MAT 233 & 250 or permission of the department

MAT 480
Advanced Topics in Mathematics

Designed to cover topics of interest that are not covered in other courses.
Prerequisites: Permission of the department

MAT 491
Seminar I (W)

A seminar in topics selected by the course instructor in which independent learning is stressed. The student is expected to present both oral and written reports on topics covered in the seminar.
Prerequisite: Junior standing and permission of the department

MAT 492
Seminar II (W)

A seminar in which each student selects a topic with the approval of the course instructor. The student is expected to present both oral and written reports. This seminar is to be taken in the final semester of the student's course work. Exceptions require the approval of the department. Prerequisite: Senior standing and permission of the department

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The Raymond Mest Math Scholarship

The Raymond Mest mathematics scholarship is awarded each fall semester to a sophomore, junior, and senior mathematics major in accordance with the following criteria.

  1. The sophomore recipient will be the student with the highest mathematics g.p.a. for courses at or above the level of Math 107. The minimum course level completed shall be Math 108 with at least one mathematics course taken at Albright College. In the event of a tie, the award will be given at the discretion of the department.
  2. The junior recipient will be the student with the highest mathematics g.p.a. for courses at or above the level of Math 107. The minimum number of mathematics courses completed shall be four (at or above the level of Math 107) with at least three taken at Albright College. In the event of a tie, the award will be given at the discretion of the department.
  3. The senior recipient will be the student with the highest mathematics g.p.a. for courses at or above the level of Math 107. The minimum number of mathematics courses completed shall be six (at or above the level of Math 107) with at least five taken at Albright College. In the event of a tie, the award will be given at the discretion of the department.

The term of the award will be for one year. The above criteria are to be used as guidelines only and are subject to change. Other factors may be used in addition to those listed above, such as, service within the department, contribution to the overall learning atmosphere, and receipt of previous award(s).

Past Recipients of the Raymond Mest Mathematics Scholarship

2010 - 2011

  • Senior: Jeff Plummer
  • Junior: Andrew Friedlund
  • Sophomore: Dustin Hill

2009-2010

  • Senior – Jennifer Werner
  • Junior – Benjamin Sporrer
  • Sophomore – Joshua Blank

2008-2009

  • Nicholas Sporrer
  • Anna Przybylski
  • Jeffrey Plummer

2007-2008

  • Jaquella Alston
  • Kristen Sawey
  • Jennifer Werner

2006-2007

  • Meghan Cowfer
  • Matthew Nomland
  • Danielle Smiley

2005-2006

  • Garrett Crouse
  • Heather Cellary
  • Erica Rubin

2004-2005

  • Howard Levin
  • Alexandra Salaneck
  • Michele Grontkowski

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