University of Pittsburgh

UNDERGRADUATE
Bulletin

School of Arts and Sciences

MAJOR AND MINOR DESCRIPTIONS BY DEPARTMENT

MATHEMATICS

The Department of Mathematics offers course work leading to a Bachelor of Science degree in mathematics as well as various courses for non-majors. Students concentrating in mathematics may pursue majors in mathematics, applied mathematics, or actuarial mathematics, or they may pursue joint majors in mathematics and economics, philosophy, or scientific computing. Each of the department’s majors has its own philosophy and its own formal requirements, so students should consult with a major advisor. For more information on these majors and the Department of Mathematics, see www.math.pitt.edu.

Major Requirements
  • Majors must complete 40 credits (see below for curriculum details on each major) with a grade of C or higher in each course for the major and at least a 2.00 GPA overall in mathematics courses. The S/NC grade option (formerly the S/N option) is not permitted.
  • MATH 0413 Introduction to Theoretical Mathematics meets the departmental W requirement.
  • Credit by examination is usually available only through the placement testing offered for incoming students.
  • Appropriate courses for the A&S-required 12-credit related area are determined in consultation with the mathematics advisor. A 12-credit related area for applied mathematics majors must be approved by the Undergraduate Committee.
  • Students considering graduate work in mathematics should be aware that many programs require a reading knowledge of one or two foreign languages from among French, German, and Russian.
  • To graduate with honors in mathematics or applied mathematics, students must meet the following requirements:
    • Completion of all mathematics requirements
    • Completion of each of the following courses with a grade of B or better:
      • MATH 1250 Abstract Algebra or (for applied mathematics majors only) 1470 Partial Differential Equations 1
      • MATH 1530 Advanced Calculus 1
      • MATH 1540 Advanced Calculus 2
      • A graduate level mathematics course
      • Completion of an honors thesis under the direction of a member of the mathematics faculty or completion of a second graduate level mathematics course in lieu of the honors thesis

The statistics requirement is waived for mathematics majors graduating with honors. Although not required, it is recommended that honors candidates take the intermediate honors courses MATH 0450 Introduction to Analysis and MATH 1185 Honors Linear Algebra during their freshman and sophomore years.

Curriculum for Actuarial Mathematics Major

Students wishing to pursue a major in Actuarial Mathematics must complete both MATH 0220 and 0230 or their equivalents with a grade of C or better before declaring actuarial mathematics as their major. Students will be required to take 63 credits, of which 45 will be in Mathematics and Statistics. Specific requirements are:

  • All of the following, totaling 12 credits: MATH 0220, 0230, and 0240 - Analytic Geometry and Calculus 1, 2, and 3
  • One of the following:
    • MATH 0280 Introduction to Matrices and Linear Algebra
    • MATH 1180 Linear Algebra 1
    • MATH 1185 Honors Linear Algebra
  • One of the following:
    • MATH 0290 Differential Equations
    • MATH 1270 Ordinary Differential Equations 1
  • Both of the following: MATH 1120 and 1121 - Actuarial Mathematics 1 and 2
  • One of the following:
    • MATH 1070 Numerical Mathematical Analysis
    • MATH 1080 Numerical Linear Algebra
  • Two of the following, totaling 6 credits:
    • MATH 1280 Ordinary Differential Equations 2
    • MATH 1360 Modeling in Applied Math 1
    • MATH 1470 Partial Differential Equations 1
    • MATH 1480 Partial Differential Equations 2
  • MATH 1110 Industrial Mathematics
  • All of the following, totaling 12 credits: ECON 0100, 0110, 1100, and 1110 - Microeconomic Theory and Macroeconomic Theory
  • One of the following:
    • CS 0401 Introduction to Computer Science
    • CS 0132 Programming in C and a Guide to the UNIX Operating System
    • CS 0007 Introduction to Computer Programming:
  • Both of the following for 6 credits: STAT 1151 Introduction to Probability and STAT 1152 Introduction to Mathematical Statistics
  • One of the following:
    • STAT 1631 Intermediate Probability
    • STAT 1731 Stochastic Processes
  • One of the following:
    • BUSFIN 1030 Introduction to Finance
    • ECON 1440 Economics of Corporation Finance

The four required Economics courses will satisfy the related area requirement.

 

Curriculum for Applied Mathematics Major

The course requirements for the applied mathematics major are distributed as follows. Since different program emphases are possible, students should consult the advisor as early as possible in regards to selection of courses:

  • All of the following, totaling 12 credits: MATH 0220, 0230, and 0240 Analytic Geometry and Calculus 1, 2, and 3
  • Both of the following, totaling 7 credits: MATH 0413 Introduction to Theoretical Mathematics and MATH 0420 Introductory Theory 1 Variable Calculus
  • One of the following: MATH 1180 Linear Algebra 1 or 1185 Honors Linear Algebra
  • The three-credit MATH 1270 Ordinary Differential Equations 1
  • One of the following, totaling 3 credits: MATH 1110 Industrial Mathematics or 1360 Modeling in Applied Math 1
  • One of the following courses:
    • MATH 1070 Numerical Mathematical Analysis
    • MATH 1080 Numerical Linear Algebra
    • MATH 1100 Linear Programming
    • MATH 1110 Industrial Mathematics
  • One of the following courses from the applied analysis group:
    • MATH 1550 Vector Analysis and Applications
    • MATH 1560 Complex Variables and Applications
    • MATH 1570 Transform Methods in Applied Math
  • One additional course from the previous two categories above, or one course from the differential equations group:
    • MATH 1280 Ordinary Differential Equations 2
    • MATH 1470 Partial Differential Equations 1
    • MATH 1480 Partial Differential Equations 2
  • Both of the following: PHYS 0174 and 0175 Basic Physics for Science and Engineering 1 and 2
  • One of the following:
    • CS 0401 Introduction to Computer Science
    • CS 0132 Programming in C and a Guide to the UNIX Operating System
    • CS 0007 Introduction to Computer Programming: Pascal
  • One of the following: STAT 1000 Applied Statistical Methods or STAT 1151 Introduction to Probability

Students interested in graduate study are strongly advised to take MATH 1530 and 1540 Advanced Calculus 1 and 2. These two courses may be substituted for the course in applied analysis and for the course specified in the eighth requirement above.

 

Curriculum for Mathematics Major

The requirements for the mathematics major are flexible so as to enable students to follow their interests. After calculus and a sequence of three basic theoretical courses, students complete the major with six or more upper-level courses. No single course may be used to fulfill two requirements. Courses for the mathematics major are distributed as follows:

  • All of the following, totaling 12 credits: MATH 0220, 0230, and 0240 Analytic Geometry and Calculus 1, 2, and 3
  • All of the following, totaling 10 credits:
    • MATH 0413 Introduction to Theoretical Mathematics
    • MATH 0420 Introductory Theory 1 Variable Calculus
    • MATH 0430 Introduction to Abstract Algebraic Systems
  • One of the following, totaling 3 credits: MATH 1180 Linear Algebra 1 or 1185 Honors Linear Algebra
  • The 3-credit MATH 1270 Ordinary Differential Equations 1
  • One of the following, totaling 3 credits:
    • MATH 1020 Applied Elementary Number Theory
    • MATH 1050 Combinatorial Mathematics
    • MATH 1240 Linear Algebra 2
    • MATH 1250 Abstract Algebra
  • Three of the following, totaling 9 credits:
    • MATH 1020 Applied Elementary Number Theory
    • MATH 1050 Combinatorial Mathematics
    • MATH 1070 Numerical Mathematical Analysis
    • MATH 1080 Numerical Linear Algebra
    • MATH 1100 Linear Programming
    • MATH 1110 Industrial Mathematics
    • MATH 1240 Linear Algebra 2
    • MATH 1250 Abstract Algebra
    • MATH 1280 Ordinary Differential Equations 2
    • MATH 1290 Topics in Geometry
    • MATH 1310 Graph Theory
    • MATH 1330 Projective Geometry
    • MATH 1350 Introduction to Differential Geometry
    • MATH 1360 Modeling in Applied Mathematics
    • MATH 1410 Introduction to Foundations of Mathematics
    • MATH 1470 Partial Differential Equations 1
    • MATH 1530 Advanced Calculus 1
    • MATH 1540 Advanced Calculus 2
    • MATH 1550 Vector Analysis and Applications
    • MATH 1560 Complex Variables and Applications
    • MATH 1570 Transform Methods in Applied Math
    • MATH 1700 Introduction to Topology
    • STAT 1631 Intermediate Probability
    • STAT 1632 Intermediate Mathematical Statistics
  • The 4-credit PHYS 0174 Basic Physics for Science and Engineering 1
Minor in Mathematics

Students wishing to pursue a minor in Mathematics must complete at least 15 credits of Mathematics coursework at the level of MATH 0250 or above. At least six (6) of these credits must be in courses numbered 1000 or above. Students must complete these requirements with an average grade of C or better.

Prerequisites for the minor:

  • MATH 0220 - Analytic Geometry and Calculus 1
  • MATH 0230 - Analytic Geometry and Calculus 2
  • MATH 0240 - Analytic Geometry and Calculus 3

Mathematics-Economics Joint Major Requirements

Students seeking a mathematics and economics joint major must adhere to the following rules and requirements:

  • Completion of at least 58 credits in mathematics and economics courses (see below for detail).
  • Earn at least a 2.00 in all courses required for the major. The S/NC option (formerly the S/N option) is not permitted.
  • The A&S 12-credit related area is not required.
  • Students should check with the departmental advisors in mathematics and economics about the required W course.
  • Students planning to do graduate study should keep in mind that many graduate programs require reading knowledge of one or two foreign languages.

The joint major provides not only a set of requirements but also suggested course sequences of mathematics and economics courses that are compatible with each other and that prepare students for various specialties. The courses to be completed are as follows:

  • Required Courses in Mathematics (31 credits)
    • MATH 0220, 0223, and 0224 Analytic Geometry and Calculus 1, 2, and 3
    • MATH 0413 Introduction to Theoretical Mathematics, 0420 Introductory Theory 1 Variable Calculus, 0430 Introduction to Abstract Algebraic Systems
    • STAT 1151 Introduction to Probability and 1152 Introduction to Mathematical Statistics
    • MATH 1180 Linear Algebra 1 or MATH 1185 Honors Linear Algebra

In addition, students are strongly recommended to take at least one field course in mathematics to be chosen from the following groups:

  • Economic Theory:
    • MATH 1100 Linear Programming
    • MATH 1250 Abstract Algebra
    • MATH 1270 Ordinary Differential Equations 1
    • MATH 1700 Introduction to Topology
  • Econometrics:
    • STAT 1221 Applied Regression
    • STAT 1311 Applied Multivariate Analysis
    • STAT 1321 Applied Time Series
    • STAT 1631 Intermediate Probability
    • STAT 1632 Intermediate Mathematical Statistics
    • STAT 1661 Linear Regression
    • STAT 1761 Game Theory
  • Mathematical Economics:
    • MATH 1100 Linear Programming
    • MATH 1270 Ordinary Differential Equations 1
    • MATH 1700 Introduction to Topology
  • Other Mathematics:
    • MATH 1070 Numerical Mathematical Analysis
    • MATH 1080 Numerical Linear Algebra
    • MATH 1110 Industrial
  • Required Courses in Economics (27 credits)
    • ECON 0100 Introduction to Microeconomic Theory
    • ECON 0110 Introduction to Macroeconomic Theory
    • ECON 1100 Intermediate Microeconomics
    • ECON 1110 Introduction to Macroeconomics
    • ECON 1150 Applied Econometrics 1 or 2150 General Econometrics; and 1140 Economic Modeling and Forecasting or 1160 Applied Econometrics 2 or 2160 Econometrics for Practitioners
    • ECON 1130 Operations Research Analysis or 1180 Mathematical Economics or 2170 Mathematical Economics
  • Six credits of field courses (This requirement may be satisfied with any field courses offered by the department except any ECON 0800 series.)

To qualify for departmental honors in the mathematics and economics joint major, students must meet the following requirements:

  • Complete the required economics courses with the added stipulation that either ECON 1180 Mathematical Economics or 2170 Mathematical Economics and a proseminar must be one of the field courses chosen.
  • Complete the following 27 credits in lieu of those normally taken:
    • MATH 0235 Honors 1 Variable Calculus
    • MATH 0240 Analytic Geometry and Calculus 3
    • MATH 0450 Introduction to Analysis
    • STAT 1151 Introduction to Probability
    • STAT 1152 Introduction to Mathematical Statistics
    • MATH 1185 Honors Linear Algebra
    • MATH 1530 Advanced Calculus 1
  • One additional 1000-level course
Maintain a GPA of at least 3.00 in mathematics courses, at least 3.25 in economics courses, and at least 3.25 overall.

 

Mathematics and Philosophy Joint Major Requirements

For the mathematics and philosophy joint major, students must take a minimum of 55 credits in a series of basic and field courses as detailed below:

  • Basic courses totaling 25 credits (presumably completed by the end of the sophomore year):
    • The basic introductory sequence in mathematics (or its equivalent), including:
      • MATH 0220, 0230, and 0240 Analytic Geometry and Calculus 1, 2, and 3
      • MATH 0413 Introduction to Theoretical Mathematics
      • MATH 0420 Introductory Theory 1 Variable Calculus
      • MATH 0430 Introduction to Abstract Algebraic Systems
    • PHIL 0200 History of Ancient Philosophy and 0210 History of Modern Philosophy. Some other introductory philosophy course may be substituted for either 0200 or 0210 with the consent of the advisor.
  • Field courses (at least 30 credits of work in upper-level mathematics and philosophy) normally distributed as follows:
    • MATH 1530 Advanced Calculus 1
    • One course from each of the following groups:
      • MATH 1540 Advanced Calculus 2
      • 1250 Abstract Algebra
      • MATH 1700 Introduction to Topology or 1290 Topics in Geometry
    • MATH 1180 Linear Algebra and one of the following:
      • MATH 1410 Introduction to Foundations of Mathematics 1
      • PHIL 1530 Set Theory
      • PHIL 1540 Computational Theory
    • Three upper-level philosophy courses (9 credits), including at least one of the following topics: philosophy of mathematics, philosophy of logic, or philosophy of science or semantics, and at least one course not concerned with any of these topics.
  • By the end of their junior year, students in this joint major are expected to have completed PHIL 1500 Symbolic Logic.
  • By the end of their senior year, students in this joint major are expected to have completed either PHIL 1520 Logical Metatheory or PHIL 1540 Computational Theory.

Mathematics and philosophy joint majors must also adhere to the following rules and requirements:

  • Students should take all required courses for letter grades. The S/NC grade (formerly the S/N option) is not an option.
  • Students should check with the advisor for courses that will meet the required W requirement.
  • Students are not required to complete the normal A&S requirement of a related area.
  • Students should keep in mind that many graduate programs require a reading knowledge of one or two foreign languages.

The mathematics and philosophy departments offer a program leading to graduation with departmental honors in the joint major. Students seeking departmental honors will be asked to prepare an oral presentation on some topic to be selected in consultation with members of the faculty. Candidates for departmental honors will be examined by a committee of three faculty members from the departments of mathematics and philosophy on their knowledge of logic and the foundations of mathematics.

 

Scientific Computing Major Requirements

The major in scientific computing consists of at least 52 credits in mathematics and computer science, including the following:

  • Basic Courses
    • MATH 0400 Discrete Mathematical Structures or CS 0441 Discrete Structures for Computer Science
    • MATH 1110 Industrial Mathematics or CS 1538 Introduction to Stimulation
    • MATH 0220, 0230, and 0240 Analytic Geometry and Calculus 1, 2, and 3
    • One of the following MATH courses:
      • 0250 Matrix Theory and Differential Equations
      • 0280 Introduction to Matrices and Linear Algebra
      • 1180 Linear Algebra 1
      • 1185 Honors Linear Algebra
    • The following CS courses:
      • 0401 Introduction to Computer Science
      • 0445 Introduction to Information Structures
      • 0447 Computer Organization and Assembly Language Programming
      • 1501 Data Structures and Algorithms
  • Advanced Courses
    • MATH 1070 Numerical Mathematical Analysis and 1080 Numerical Linear Algebra
    • One of the following MATH courses:
      • 1100 Linear Programming
      • 1270 Ordinary Differential Equations 1
      • 1470 Partial Differential Equations 1
    • CS 1566 Introduction to Computer Graphics and CS 1645 Introduction to High Performance Computing Systems
    • One of the following CS courses:
      • 1510 Design and Analysis of Algorithms
      • 1520 Programming Languages
      • 1530 Software Engineering
      • 1541 Introduction to Computer Architecture
      • 1555 Database Management Systems
  • Scientific computing majors must also follow these rules and requirements to complete the major:
    • Students must complete at least 12 credits in a related area of physical or biological science, economics, or an approved area of engineering. The course sequence must be approved by the Program Committee.
    • A grade of C or higher is required in each course for the major.
    • Students contemplating graduate study should discuss with their advisor as early as possible the additional courses they should take to prepare for graduate study in their desired area.
The departmental W course requirement may be satisfied by MATH 1110 Industrial Mathematics. Certain required computer science (CS) courses may occasionally be offered as W courses, but CS W-designated courses vary from term to term.