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MATHEMATICS

The Department of Mathematics offers course work leading to a Bachelor of Science degree in mathematics as well as various courses for nonmajors. Students concentrating in mathematics may pursue majors in mathematics or applied mathematics, or pursue joint majors in mathematics-economics, mathematics-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 and read the Student Handbook for Majors and Joint Majors, available from the departmental office. For more information on these majors and the Department of Mathematics, see http://www.math.pitt.edu/.

Shared Requirements for Mathematics and Applied Mathematics

The mathematics department offers a major in mathematics and a major in applied mathematics. Each of those majors is subject to the following shared rules and 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 QPA overall in mathematics courses. The S/N grade 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 CAS 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 and Applications)
    • MATH 1530 (Advanced Calculus 1)
    • MATH 1540 (Advanced Calculus 2)
    • MATH 1800 (Advanced Topics in Mathematics) or 1801 (Advanced Topics in Mathematics)
    • Completion of an honors thesis under the direction of a member of the mathematics faculty or completion of a second course from the pair 1800/1801 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 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, 0240 (Analytic Geometry and Calculus 1, 2, 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 three credits: MATH 1180 or 1185 (Linear Algebra 1 or Honors Linear Algebra)

• The three-credit MATH 1270 (Ordinary Differential Equations 1)

• One of the following, totaling three 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 nine credits:
  • MATH 1020 (Applied Elementary Number Theory)
  • MATH 1050 (Combinatorial Mathematics)
  • MATH 1070 (Numerical Analysis)
  • MATH 1080 (Numerical Linear Algebra)
  • MATH 1100 (Linear Programming)
  • MATH 1110 (Industrial Numerical Analysis)
  • 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 and Applications)
  • 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)
  • MATH 1800 (Advanced Topics in Mathematics)
  • MATH 1801 (Advanced Topics in Mathematics)
  • STAT 1631 (Intermediate Math Statistics)
  • STAT 1632 (Intermediate Math Statistics 2)

• The three-credit PHYS 0104 (Basic Physics for Science and Engineering 1)

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:

1. All of the following, totaling 12 credits: MATH 0220, 0230, 0240 (Analytic Geometry and Calculus 1, 2, 3)

2. Both of the following, totaling 7 credits: MATH 0413 (Introduction to Theoretical Mathematics) and MATH 0420 (Introductory Theory 1- Variable Calculus)

3. One of the following: MATH 1180 or 1185 (Linear Algebra 1 or Honors Linear Algebra)

4. The three-credit MATH 1270 (Ordinary Differential Equations 1)

5. One of the following, totaling three credits: MATH 1110 (Industrial Numerical Analysis) or 1360 (Modeling in Applied Mathematics)

6. One of the following courses:
   • MATH 1070 (Numerical Analysis)
   • MATH 1080 (Numerical Linear Algebra)
   • MATH 1100 (Linear Programming)
   • MATH 1110 (Industrial Numerical Analysis)

7. 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)

8. One additional course from number six (6) or number seven (7) above, or one course from the Differential Equations Group:
   • MATH 1280 (Ordinary Differential Equations 2)
   • MATH 1470 (Partial Differential Equations and Applications)
   • MATH 1480 (Partial Differential Equations 2)

9. Both of the following: PHYS 0104 and 0105 (Basic Physics for Science and Engineering 1 and 2)

10. 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)

11. One of the following: STAT 1000 (Applied Statistical Methods) or STAT 1151 (Introduction to Probability Statistics 1)

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 (7), and for the course specified in number eight (8) above.

Mathematics-Economics Joint Major Requirements

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

• Completion of at least 61 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/N option is not permitted.
• The CAS 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 which are compatible with each other and which 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 Algebra)
  • STAT 1151 and 1152 (Introduction to Mathematics Statistics 1 and 2)
  • 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 1110 (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 Math Statistics 1)
  • STAT 1632 (Intermediate Math Statistics 2)
  • STAT 1661 (Progression Model and Linear Theory 1)
  • 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 Analysis)
  • MATH 1080 (Numerical Linear Algebra)
  • MATH 1110 (Industrial Numerical Analysis)
• Required Courses in Economics (30 credits)
  • ECON 0100 (Introduction to Microeconomic Theory)
  • ECON 0110 (Introduction to Macroeconomic Theory)
  • ECON 1100 (Intermediate Microeconomic Theory)
  • ECON 1110 (Introduction to Macroeconomic Theory)
  • 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)
  • Nine credits of field courses. This requirement may be satisfied with any field courses offered by the department except the following: ECON 0800 (Introduction to Economics); 0150 (Socialism Versus Capitalism); 1170 (Mathematics for Economists); or any course used to satisfy any of the economics course requirements above).

To qualify for departmental honors in the mathematics-economics 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 pro-seminar must be one of the field courses chosen.

• Complete the following 27 credits in lieu of those normally taken:
  • MATH 0235 (UHC 1 - Variable Calculus)
  • MATH 0240 (UHC Analytic Geometry and Calculus 3)
  • MATH 0450 (UHC introduction to Analysis)
  • STAT 1151 (Introduction to Probability Statistics 1)
  • STAT 1152 (Introduction to Probability Statistics 2)
  • MATH 1185 (UHC Linear Algebra)
  • MATH 1530 (Advanced Calculus)
  • One additional 1000-level course
• Maintain a QPA of at least 3.00 in mathematics courses, at least 3.25 in economics courses, and at least 3.25 overall.

Mathematics-Philosophy Joint Major Requirements

For the mathematics-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 Algebra)
  • 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)
    • MATH 1180 (Linear Algebra) or 1250 (Abstract Algebra)
    • MATH 1700 (Introduction to Topology)
      or 1290 (Topics in Geometry)
  • MATH 1410 and 1420 (Introduction to Foundations of Mathematics 1 and 2)
  • 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.

  Note: By the end of the junior year, students in the joint major are expected to have completed PHIL 1500 (Symbolic Logic). By the end of the senior year, students are expected to have completed 1520 (Logical Metatheory).

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

  • Students should take all required courses for letter grades. The S/N grade 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 CAS 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 Overview

The scientific computing major, offered jointly by the Department of Computer Science and the Department of Mathematics, is an excellent choice for students interested in computer science and applied mathematics who desire an exciting and stimulating career in industry or a research laboratory. Scientific computing studies the modeling, visualization, and computational stimulation of physical processes. The major synthesizes the revolutionary advances in computer technology and the algorithms of computational mathematics and focuses these powerful tools on practical problems.

The major's approach to design, prediction, control, and optimization is flexible, powerful, and inexpensive, and so it is little wonder that there is a demand for specialists trained in this area. Specialists in the emerging field of scientific computing are employed in industry and research laboratories dealing with scientific, engineering, and technological problems. They are key members of research and development teams dealing with modeling, design, stimulation, optimization, and control of practical problems. The scientific computing degree will provide a strong background, balanced between computational mathematics and applied computer science, for students seeking a career in scientific computing. With careful choice of electives, it also prepares a student for graduate study in computer science and computational 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 Mathematics) and 1080 (Numerical Linear Algebra)
  • One of the following MATH courses:
    • 1100 (Linear Programming)
    • 1270 (Ordinary Differential Equations)
    • 1470 (Partial Differential Equations and Applications)
  • CS 1566 (Introduction to Computer Graphics) and CS 1645 (Introduction to High Performance Computing)
  • One of the following CS courses:
    • 1510 (Design and Analysis of Algorithms)
    • 1520 (Programming Languages)
    • 1530 (Software Engineering)
    • 1541 (Introduction to Computer Architecture)
    • 1555 (Data Base 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.

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