Dietrich 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.mathematics.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 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 Dietrich School -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 second 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 s 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
- MATH 0220 Analytic Geometry and Calculus 1
- MATH 0230 Analytic Geometry and Calculus 2
- MATH 0240 - Analytic Geometry and Calculus 3
- One of the following courses.
- MATH 0413 Introduction to Theoretical Mathematics
- MATH 0450 Introduction to Analysis
- One of the following courses.
- MATH 1180 Linear Algebra 1
- MATH 1185 Honors Linear Algebra
- MATH 1270 Ordinary Differential Equations 1
- Both of the following courses.
- MATH 1120 Actuarial Mathematics 1
- MATH 1121 Actuarial Mathematics 2
- One of the following courses.
- MATH 1070 Numerical Mathematical Analysis
- MATH 1080 Numerical Linear Algebra
- Two of the following courses.
- MATH 1100 Linear Programming
- MATH 1110 Industrial Mathematics (writing-intensive course)
- MATH 1122 Actuarial Mathematics 3
- MATH 1280 Ordinary Differential Equations 2
- MATH 1360 Modeling in Applied Math 1
- MATH 1470 Partial Differential Equations 1
- MATH 1530 Advanced Calculus 1
- MATH 1540 Advanced Calculus 2
- MATH 1550 Vector Analysis
- Both of the following courses.
- ECON 0100 Intermediate Microeconomic Theory
- ECON 0110 Intermediate Macroeconomic Theory
- One of the following:
- CS 0004 Introduction to Computer Programming in BASIC
- CS 0401 Introduction to Computer Science
- STAT 1301 Statistical Packages
- BUSMIS 1060 Introduction to Information Systems
- ENGR 0012 Introduction to Engineering Computing
- Both of the following courses.
- STAT 1000 Applied Statistical Methods
- STAT 1151 Introduction to Probability One of the following courses.
- ECON 1150 Econometrics
- STAT 1221 Applied Regression
- One of the following courses.
- STAT 1321 Times Series
- STAT 1731 Stochastic Processes
- STAT 1741 Applied Probability
- One of the following courses.
- BUSFIN 1311 Corporate 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 courses.
- MATH 0220 Analytic Geometry and Calculus 1
- MATH 0230 Analytic Geometry and Calculus 2
- MATH 0240 Analytic Geometry and Calculus 3
- Both of the following courses.
- MATH 0413 Introduction to Theoretical Mathematics
- MATH 0420 Introductory Theory 1 Variable Calculus
- One of the following courses.
- MATH 1180 Linear Algebra 1
- MATH 1185 Honors Linear Algebra
- MATH 1270 Ordinary Differential Equations 1
- One of the following courses.
- MATH 1110 Industrial Mathematics
- MATH 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 courses.
- PHYS 0174 Basic Physics for Science and Engineering
- PHYS 0175 Basic Physics for Science and Engineering 2
- One of the following courses.
- CS 0007 Introduction to Computer Programming
- CS 0132 Programming in C and a Guide to the UNIX Operating System
- CS 0401 Introduction to Computer Science
- One of the following courses.
- STAT 1000 Applied Statistical Methods
- STAT 1151 Introduction to Probability
Curriculum for Mathematical Biology
Students pursuing the Mathematical Biology major are encouraged to take CHEM 0110 General Chemistry 1 and CHEM 0120 General Chemistry 2, as these courses will satisfy the Dietrich School of Arts and Sciences breadth requirement in natural science and will expand their biology and neuroscience course options. Several of the BIOSC courses that fulfill requirements for this major have prerequisites, but some do not have prerequisites. PHYS 0174 Basic Physics for Science and Engineering 1 and PHYS 0175 Basic Physics for Science and Engineering 2 also carry a high degree of relevance for Mathematical Biology majors.
The Mathematical Biology major will require the completion of 43 credits in mathematics.
- Three Calculus courses
- MATH 0220 Analytic Geometry and Calculus 1
- MATH 0230 Analytic Geometry and Calculus 2
- MATH 0240 Analytic Geometry and Calculus 3
- Two introductory theoretical courses
- MATH 0413 Introduction to Theoretical Mathematics*
- MATH 0420 Introduction to Theory 1 – Variable Calculus*
*Note: Qualified students may substitute MATH 0450 Honors Analysis for MATH 0413 and MATH 0420.
- One of the following courses.
- MATH 1180 Linear Algebra 1
- MATH 1185 Honors Linear Algebra 1
- One of the following courses.
- MATH 1270 Ordinary Differential Equations 1
- MATH 1275 Honors Ordinary Differential Equations 1
- Two mathematical biology courses
- MATH 1370 Introduction to Computational Neuroscience
- MATH 1380 Mathematical Biology
- Two numerical mathematics courses
- MATH 1070 Numerical Mathematical Analysis
- MATH 1080 Numerical Linear Algebra
- Two applied analysis courses from the following list
- MATH 1280 Ordinary Differential Equations 2
- MATH 1470 Partial Differential Equations 1
- MATH 1530 Advanced Calculus 1
- MATH 1550 Vector Analysis and Applications
- MATH 1560 Complex Variables and Applications
- Four Biology or Neuroscience courses
- BIOSC 0150 Foundations of Biology 1
- BIOSC 0160 Foundations of Biology 2
- Two of the following; at least one must be at the 1000 level
- BIOSC 0350 Genetics or BIOSC 0355 Honors Genetics
- BIOSC 0370 Ecology
- BIOSC 1000 Introductory Biochemistry
- One of the following courses
- BIOSC 1070 Human Physiology
- BIOSC 1250 Human Physiology
- BIOSC 1870 Animal Physiology
- BIOSC 1130 Evolution
- BIOSC 1320 Population Biology
- BIOSC 1470 Biophysical Chemistry
- BIOSC 1500 Cell Biology
- BIOSC 1520 Developmental Biology
- BIOSC 1540 Computational Biology
- BIOSC 1760 Immunology
- NROSCI 0080 Brain and Behavior
- NROSCI 1000 Introduction to Neuroscience or NROSCI 1003 Honors Introduction to Neuroscience
- NROSCI 1011 Functional Neuroanatomy
- NROSCI 1012 Neurophysiology
- NROSCI 1017 Synaptic Transmission
- NROSCI 1034 Neural Basis of Cognition
- STAT 1000 Applied Statistical Methods
Mathematical Biology students who plan to continue in graduate studies are advised to take advanced calculus, MATH 1530 Advance Calculus 1 and MATH 1540 Advanced Calculus 2. MATH 1370 Introduction to Computational Neuroscience and MATH 1380 Mathematical Biology introduce students to techniques for independent research; students in these courses are encouraged to pursue research opportunities in Mathematical Biology that are available locally and nationally.
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 courses
- MATH 0220 Analytic Geometry and Calculus 1
- MATH 0230 Analytic Geometry and Calculus 2, and 3
- Math 0240 Analytic Geometry and Calculus 3
- All of the following courses
- MATH 0413 Introduction to Theoretical Mathematics
- MATH 0420 Introductory Theory 1 Variable Calculus
- MATH 0430 Introduction to Abstract Algebraic Systems
- One of the following courses
- MATH 1180 Linear Algebra 1
- MATH 1185 Honors Linear Algebra
- t MATH 1270 Ordinary Differential Equations 1
- One of the following courses s:
- 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 1420 Foundations of Mathematics 2
- MATH 1470 Partial Differential Equations 1
- MATH 1510 Probability
- 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
- Any three credit graduate level MATH course
- STAT 1631 Intermediate Probability
- STAT 1632 Intermediate Mathematical Statistics
- 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 is not permitted.
- The Dietrich School 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 second 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 follows
- Required Courses in Mathematics
- MATH 0220 Analytic Geometry and Calculus 1
- MATH 0223 Analytic Geometry and Calculus 2
- MATH 0224 Analytic Geometry and Calculus 3
- MATH 0413 Introduction to Theoretical Mathematics
- MATH 0420 Introductory Theory 1 Variable Calculus
- One of the following courses.
MATH 1180 Linear Algebra 1
MATH 1185 honors Linear Algebra
- STAT 1151 Introduction to Probability
- STAT 1152 Introduction to Mathematical Statistics
In addition, students are encouraged to take at least one field course in mathematics from the following list.
- MATH 1100 Linear Programming
- MATH 1110 Industrial Mathematics
- MATH 1470 Partial Differential Equations 1
- MATH 1530 Advanced Calculus 1
- MATH 1540 Advanced Calculus 2
- MATH 1550 Vector Analysis and Applications
- MATH 1700 Introduction to Topology
- STAT 1221 Applied Regression
- STAT 1311 Applied Multivariate Analysis
- STAT 1321 Applied Time Series
- STAT 1631 Intermediate Probability
- STAT 1632 Intermediate Mathematical Statistics
- STAT 1761 Game Theory
- 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
- ECON 1200 Introduction to Game Theory
- One ECON non-0800 series elective course
- Two ECON 1000-level courses that require either ECON 1100 or ECON 1110 as a prerequisite
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 ECON 1180 Mathematical Economics and a proseminar be one of the field courses chosen.
- Complete the following courses in lieu of those normally taken:
- MATH 0235 Honors 1 Variable Calculus
- MATH 0240 Analytic Geometry and Calculus 3
- MATH 0450 Introduction to Analysis
- MATH 1185 Honors Linear Algebra
- MATH 1530 Advanced Calculus 1
- STAT 1151 Introduction to Probability
- STAT 1152 Introduction to Mathematical Statistics
- 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 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 Dietrich School requirement of a related area.
- Students should keep in mind that many graduate programs require a reading knowledge of one or two second 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.