# Mathematics

*Bachelor of Arts Degree: 180.0 quarter credits
*

*Bachelor of Science Degree: 180 quarter credits*

## About the Program

The mathematics major at Drexel provides a supportive learning environment in which students obtain a firm grounding in the core areas of mathematics and apply this knowledge to problems encountered in a technological society. The Department of Mathematics offers students the option of either a BA or a BS degree.

The Mathematics Department takes pride in offering a balanced and flexible curriculum. Three very different kinds of skills are emphasized in the mathematics major:

**Abstract Reasoning**

All students majoring in mathematics take courses that emphasize abstract reasoning. Students read and write proofs, and graduate well prepared to enter a PhD program in mathematics.

**Computing**

All students majoring in mathematics take a series of computing courses. This emphasis on computing is one of the distinctive features of the mathematics program at Drexel, and provides students with a competitive advantage in the job market.

**Mathematical Modeling**

All students majoring in mathematics take multidisciplinary courses that focus on the interplay between mathematics and an area of application.

Students often use electives to focus on an area of personal interest. The Department of Mathematics encourages students to minor in a subject where mathematics is applied. The Department provides an advisor to assist students in selecting electives and planning career paths.

## Degree Requirements (BA)

General Education Requirements | ||

COM 230 | Techniques of Speaking | 3.0 |

ENGL 101 | Expository Writing and Reading | 3.0 |

ENGL 102 | Persuasive Writing and Reading | 3.0 |

ENGL 103 | Analytical Writing and Reading | 3.0 |

UNIV H101 | The Drexel Experience | 2.0 |

One of the following Computer Science sequences: | 9.0 | |

Option I | ||

Special Topics in Computer Science (Introduction to Programming with Media: Python ) | ||

Special Topics in Computer Science ( Computer Programming Fundamentals) | ||

Computer Programming I | ||

Option II | ||

Special Topics in Computer Science (Introduction to Programming with Media: Python ) | ||

Computer Programming I | ||

Computer Programming II | ||

Humanities and fine arts electives | 6.0 | |

International studies electives | 6.0 | |

Science electives | 8.0 | |

Social and behavioral sciences electives | 6.0 | |

Studies in diversity electives | 6.0 | |

Free Electives (depending upon other options selected) | 64.0 | |

Core Mathematics Requirements | ||

MATH 121 | Calculus I ^{*} | 4.0 |

MATH 122 | Calculus II | 4.0 |

MATH 123 | Calculus III | 4.0 |

MATH 200 | Multivariate Calculus | 4.0 |

MATH 201 | Linear Algebra | 4.0 |

MATH 210 | Differential Equations | 4.0 |

MATH 220 | Introduction to Mathematical Reasoning | 3.0 |

MATH 331 | Abstract Algebra I | 3.0-4.0 |

or MATH 401 | Elements of Modern Analysis I | |

Additional Mathematics Requirements | ||

Track Courses | 9.0-11.0 | |

Select one of the following sequences: | ||

Discrete Mathematics and Mathematical Applications of Symbolic Software and Abstract Algebra II | ||

Vector Calculus and Complex Variables and Elements of Modern Analysis II | ||

Numerical Analysis I and Numerical Analysis II and Introduction to Optimization Theory | ||

Probability and Statistics I and Probability and Statistics II and Mathematical Applications of Statistical Software | ||

Survey of Geometry and Probability and Statistics I and Probability and Statistics II | ||

Four Mathematics Courses ^{**} | 12.0 | |

Three Mathematics Related Courses ^{***} | 9.0 | |

Total Credits | 180.0 |

* | Math majors must pass MATH 121 with a grade of B or higher. |

** | Students either select these courses from the list of MATH courses in for the BS in Mathematics or from additional mathematics electives, provided that approval is obtained |

*** | Students must complete three additional courses in fields related to mathematics such as science, engineering, economics, finance, decision sciences, and computer science. A list of approved courses will be maintained by the undergraduate mathematics advisor. These three courses are in addition to the two science courses required as part of the General Education requirements, as well as the CS 131-133 required sequence. |

**Categories of Electives**

*Humanities and arts electives*

Designated courses in art, art history, communication studies, foreign languages (300-level or above), history, literature, music, philosophy, religion, and theatre arts.

*International electives*

Designated courses in anthropology, art history, history, literature, music, politics and sociology. Courses with an international focus may be used to fulfill requirements in other categories as well.

*Science electives*

Students select two courses from chemistry, biology or physics. both courses may be in the same subject or they may be in different subject areas.

*Social and behavioral sciences electives*

Designated courses in anthropology, economics, criminal justice, international relations, history, politics, psychology and sociology.

*Studies in diversity electives*

Designated courses in Africana studies, anthropology, communication, English, history, Judaic studies, linguistics, music, sociology and women's studies.

### Writing-Intensive Course Requirements

In order to graduate, all students must pass three writing-intensive courses after their freshman year. Two writing-intensive courses must be in a student's major. The third can be in any discipline. Students are advised to take one writing-intensive class each year, beginning with the sophomore year, and to avoid “clustering” these courses near the end of their matriculation. Transfer students need to meet with an academic advisor to review the number of writing-intensive courses required to graduate.

A "WI" next to a course in this catalog may indicate that this course can fulfill a writing-intensive requirement. For the most up-to-date list of writing-intensive courses being offered, students should check the Writing Intensive Course List at the University Writing Center. Students scheduling their courses can also conduct a search for courses with the attribute "WI" to bring up a list of all writing-intensive courses available that term. Transfer students need to meet with an academic advisor to review the number of writing-intensive courses required to graduate.

## Sample Plan of Study (BA)

### 5-year co-op sequence

Term 1 | Credits | |
---|---|---|

ENGL 101 | Expository Writing and Reading | 3.0 |

MATH 121 | Calculus I | 4.0 |

UNIV H101 | The Drexel Experience | 1.0 |

Computer Science (CS) sequence course^{*} | 3.0 | |

Science elective | 4.0 | |

Term Credits | 15.0 | |

Term 2 | ||

ENGL 102 | Persuasive Writing and Reading | 3.0 |

MATH 122 | Calculus II | 4.0 |

UNIV H101 | The Drexel Experience | 1.0 |

Computer Science (CS) sequence course^{*} | 3.0 | |

Science elective | 4.0 | |

Term Credits | 15.0 | |

Term 3 | ||

ENGL 103 | Analytical Writing and Reading | 3.0 |

MATH 123 | Calculus III | 4.0 |

MATH 220 | Introduction to Mathematical Reasoning | 3.0 |

Computer Science (CS) sequence course^{*} | 3.0 | |

Social science elective | 3.0 | |

Term Credits | 16.0 | |

Term 4 | ||

COM 230 | Techniques of Speaking | 3.0 |

MATH 200 | Multivariate Calculus | 4.0 |

MATH 201 | Linear Algebra | 4.0 |

Diversity studies elective | 3.0 | |

International studies elective | 3.0 | |

Term Credits | 17.0 | |

Term 5 | ||

Mathematics (MATH) course^{*} | 3.0 | |

Course in math-related field^{**} | 3.0 | |

Humanities/Fine arts elective | 3.0 | |

Free electives | 6.0 | |

Term Credits | 15.0 | |

Term 6 | ||

MATH 210 | Differential Equations | 4.0 |

Mathematics (MATH) course^{*} | 3.0 | |

Social science elective | 3.0 | |

Humanities/Fine arts elective | 3.0 | |

Free elective | 3.0 | |

Term Credits | 16.0 | |

Term 7 | ||

Mathematics (MATH) sequence option^{*} | 3.0 | |

Diversity studies elective | 3.0 | |

Free electives | 9.0 | |

Term Credits | 15.0 | |

Term 8 | ||

MATH 401 or 331 | Elements of Modern Analysis I Abstract Algebra I | 3.0 |

Course in a math-related field^{**} | 3.0 | |

International studies elective | 3.0 | |

Free electives | 6.0 | |

Term Credits | 15.0 | |

Term 9 | ||

Mathematics sequence option^{*} | 3.0 | |

Course in a math-related field^{**} | 3.0 | |

Free electives | 9.0 | |

Term Credits | 15.0 | |

Term 10 | ||

Mathematics (MATH) course^{*} | 4.0 | |

Free electives | 12.0 | |

Term Credits | 16.0 | |

Term 11 | ||

Mathematics sequence option^{*} | 3.0 | |

Free electives | 10.0 | |

Term Credits | 13.0 | |

Term 12 | ||

Mathematics (MATH) course^{*} | 3.0 | |

Free electives | 9.0 | |

Term Credits | 12.0 | |

Total Credit: 180.0 |

* | See degree requirements. |

** | Students must complete three courses in fields related to mathematics such as science, engineering, economics, finance, decision sciences, and computer science. A list of approved courses will be maintained by the undergraduate mathematics advisor. These three courses are in addition to the two science courses required as part of the General Education requirements, as well as the Computer Science (CS) required sequence. |

## Degree Requirements (BS)

General Education Requirements | ||

COM 230 | Techniques of Speaking | 3.0 |

ENGL 101 | Composition and Rhetoric I: Inquiry and Exploratory Research | 3.0 |

ENGL 102 | Composition and Rhetoric II: The Craft of Persuasion | 3.0 |

ENGL 103 | Composition and Rhetoric III: Thematic Analysis Across Genres | 3.0 |

UNIV S101 | The Drexel Experience | 2.0 |

One of the following Computer Science sequences: | 9.0 | |

Option I | ||

Intro Multimedia Programming | ||

Computer Programming Fundamentals | ||

Computer Programming I | ||

Option II | ||

Intro Multimedia Programming | ||

Computer Programming I | ||

Computer Programming II | ||

Any Biology (BIO) course | 3.0-4.0 | |

Any Chemistry (CHEM) course | 3.0-4.0 | |

Any Physics (PHYS) course | 3.0-4.0 | |

Humanities electives | 9.0 | |

Social sciences electives | 18.0 | |

Free electives | 41.0 | |

Mathematics Requirements | ||

MATH 121 | Calculus I ^{*} | 4.0 |

MATH 122 | Calculus II | 4.0 |

MATH 123 | Calculus III | 4.0 |

MATH 200 | Multivariate Calculus | 4.0 |

MATH 201 | Linear Algebra | 4.0 |

MATH 210 | Differential Equations | 4.0 |

MATH 220 | Introduction to Mathematical Reasoning | 3.0 |

MATH 331 | Abstract Algebra I | 4.0 |

MATH 332 | Abstract Algebra II | 3.0 |

MATH 401 | Elements of Modern Analysis I | 3.0 |

MATH 402 | Elements of Modern Analysis II | 3.0 |

Math Major Electives | 40.0 | |

Select a minimum of 40 credits (10-14 classes) from the following: | ||

Survey of Geometry | ||

Discrete Mathematics | ||

Math Competition Problem Solving Seminar | ||

History of Mathematics | ||

Differential Equations II | ||

Complex and Vector Analysis for Engineers | ||

Numerical Analysis I | ||

Numerical Analysis II | ||

Introduction to Optimization Theory | ||

Probability and Statistics I | ||

Probability and Statistics II | ||

Mathematical Applications of Symbolic Software | ||

Mathematical Applications of Statistical Software | ||

Techniques of Data Analysis | ||

Actuarial Mathematics | ||

Vector Calculus | ||

Complex Variables | ||

Partial Differential Equations | ||

Linear Algebra II | ||

Introduction to Topology | ||

Mathematical Finance | ||

Cryptography | ||

Total Credits | 180.0-183.0 |

* | Math majors must pass MATH 121 with a grade of B or higher. |

### Writing-Intensive Course Requirements

In order to graduate, all students must pass three writing-intensive courses after their freshman year. Two writing-intensive courses must be in a student's major. The third can be in any discipline. Students are advised to take one writing-intensive class each year, beginning with the sophomore year, and to avoid “clustering” these courses near the end of their matriculation. Transfer students need to meet with an academic advisor to review the number of writing-intensive courses required to graduate.

A "WI" next to a course in this catalog may indicate that this course can fulfill a writing-intensive requirement. For the most up-to-date list of writing-intensive courses being offered, students should check the Writing Intensive Course List at the University Writing Center. Students scheduling their courses can also conduct a search for courses with the attribute "WI" to bring up a list of all writing-intensive courses available that term. Transfer students need to meet with an academic advisor to review the number of writing-intensive courses required to graduate.

## Sample Plan of Study (BS)

This a recommended plan, illustrating the five-year co-op sequence. Additional recommended plans of study for other co-op options are available from the department.

Term 1 | Credits | |
---|---|---|

ENGL 101 | Composition and Rhetoric I: Inquiry and Exploratory Research | 3.0 |

MATH 121 | Calculus I | 4.0 |

UNIV S101 | The Drexel Experience | 2.0 |

Computer Science (CS) sequence course^{*} | 3.0 | |

Any Biology (BIO) course | 3.0-4.0 | |

Term Credits | 15.0-16.0 | |

Term 2 | ||

ENGL 102 | Composition and Rhetoric II: The Craft of Persuasion | 3.0 |

MATH 122 | Calculus II | 4.0 |

Computer Science (CS) sequence course^{*} | 3.0 | |

Any Chemistry (CHEM) course | 3.0-4.0 | |

Term Credits | 13.0-14.0 | |

Term 3 | ||

ENGL 103 | Composition and Rhetoric III: Thematic Analysis Across Genres | 3.0 |

MATH 123 | Calculus III | 4.0 |

MATH 200 | Multivariate Calculus | 4.0 |

Computer Science (CS) sequence course^{*} | 3.0 | |

Any Physics (PHYS) course | 3.0-4.0 | |

Term Credits | 17.0-18.0 | |

Term 4 | ||

COM 230 | Techniques of Speaking | 3.0 |

MATH 201 | Linear Algebra | 4.0 |

MATH 220 | Introduction to Mathematical Reasoning | 3.0 |

Social science electives | 6.0 | |

Term Credits | 16.0 | |

Term 5 | ||

MATH 210 | Differential Equations | 4.0 |

Mathematics (MATH) elective^{**} | 3.0 | |

Social science elective | 3.0 | |

Humanities elective | 3.0 | |

Term Credits | 13.0 | |

Term 6 | ||

MATH 331 | Abstract Algebra I | 4.0 |

Mathematics (MATH) elective^{**} | 4.0 | |

Social science elective | 3.0 | |

Humanities elective | 3.0 | |

Term Credits | 14.0 | |

Term 7 | ||

MATH 332 | Abstract Algebra II | 3.0 |

Mathematics (MATH) elective^{**} | 4.0 | |

Humanities elective | 3.0 | |

Social science elective | 3.0 | |

Free elective | 3.0 | |

Term Credits | 16.0 | |

Term 8 | ||

MATH 401 | Elements of Modern Analysis I | 3.0 |

Mathematics (MATH) elective^{**} | 3.0 | |

Social science elective | 3.0 | |

Free electives | 6.0 | |

Term Credits | 15.0 | |

Term 9 | ||

MATH 402 | Elements of Modern Analysis II | 3.0 |

Mathematics (MATH) electives^{**} | 7.0 | |

Free electives | 6.0 | |

Term Credits | 16.0 | |

Term 10 | ||

Mathematics (MATH) electives^{**} | 8.0 | |

Free electives | 7.0-8.0 | |

Term Credits | 15.0-16.0 | |

Term 11 | ||

Mathematics (MATH) electives^{**} | 7.0 | |

Free electives | 8.0 | |

Term Credits | 15.0 | |

Term 12 | ||

Mathematics (MATH) electives^{**} | 6.0 | |

Free electives | 9.0-10.0 | |

Term Credits | 15.0-16.0 | |

Total Credit: 180.0-185.0 |

* | See degree requirements. |

** | Select from MATH 205, MATH 221, MATH 235, MATH 238, MATH 285, MATH 291, MATH 300, MATH 301, MATH 305, MATH 311, MATH 312, MATH 316, MATH 318 [WI] , MATH 319, MATH 320, MATH 321, MATH 322, MATH 323, MATH 387, MATH 422, MATH 449,MATH 475. |

## Co-op/Career Opportunities

Mathematicians are employed in a variety of capacities in business, industry, and government. Students can combine courses in economics or finance and mathematics to prepare for careers in the actuarial field, banks, stock exchanges, or finance departments of large corporations or other financial institutions. Students interested in science careers may focus on probability and statistics in order to work for industries like pharmaceutical manufacturers. Many others combine math studies with computer science courses to prepare for careers in information systems or engineering.

Teacher certification is also a career option available through a joint program in mathematics and teacher education.

Visit the Drexel Steinbright Career Development Center for more detailed information on co-op and post-graduate opportunities.

## Dual Degree Bachelor’s Programs

Since applied mathematics plays an important role in many different disciplines, mathematics majors often choose to pursue specialization in a second field of study. Students may choose a dual major that involves completing the requirements of two separate majors or they can opt for a minor, which involves completing the major in one field and a smaller set of courses in another.

Dual majors are common in mathematics/computer science and mathematics/physics. Students interested in a dual major should consult with their advisor or contact the assistant department head. Dual majors in other fields are also possible, but early planning and discussions with advisors is essential.

## Minor in Mathematics

The minor in mathematics consists of five required courses and at least 18.0 credits of electives from a specified group of elective courses specified below.

Required Courses | ||

MATH 121 | Calculus I | 4.0 |

MATH 122 | Calculus II | 4.0 |

MATH 123 | Calculus III | 4.0 |

MATH 200 | Multivariate Calculus | 4.0 |

MATH 201 | Linear Algebra ^{*} | 3.0-4.0 |

or MATH 261 | Linear Algebra | |

Mathematics Minor Electives ^{**} | ||

Select six of the foll0wing: | 19.0-20.0 | |

Survey of Geometry | ||

Differential Equations ^{*} | ||

or MATH 262 | Differential Equations | |

Introduction to Mathematical Reasoning | ||

Discrete Mathematics | ||

Math Competition Problem Solving Seminar | ||

Differential Equations II | ||

Applied Differential Equations | ||

Complex and Vector Analysis for Engineers ^{***} | ||

Numerical Analysis I | ||

Numerical Analysis II | ||

Introduction to Optimization Theory | ||

Probability and Statistics I | ||

Probability and Statistics II | ||

Mathematical Applications of Symbolic Software | ||

Mathematical Applications of Statistical Software | ||

Actuarial Mathematics | ||

Vector Calculus | ||

Complex Variables | ||

Partial Differential Equations | ||

Abstract Algebra I | ||

Abstract Algebra II | ||

Elements of Modern Analysis I | ||

Elements of Modern Analysis II | ||

Scientific Data Analysis I | ||

Scientific Data Analysis II | ||

Introduction to Topology | ||

Mathematical Finance | ||

Introduction to Graph Theory | ||

Cryptography | ||

Total Credits | 38.0-40.0 |

* | Students count only one of these two courses for their minor. |

** | A request form is available for any other mathematics courses upon the written approval prior to the beginning of the quarter in which the course is to be offered. Students should contact the department's academic advisor, Professor Marna Mozeff for further information. Professor Mozeff can be reached at 215.895.6691 or marna.a.mozeff@drexel.edu. |

*** | Students who take MATH 291 cannot also count MATH 321 or MATH 322 toward their minor. |

### Courses

**MATH 004 Trigonometry 0.0 Credits**

Required for all students who did not have high school trigonometry and for those who did not pass the placement test in trigonometry. Covers the rectangular coordinate system and distance formula, angular measure and trigonometric functions of a number, variations and graphs of the trigonometric functions, trigonometric identities and equations, inverse trigonometric functions, and solutions of triangles applications. All terms.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**MATH 050 Elements of Precalculus 0.0 Credits**

This course covers topics essential for the study of calculus, including elements of algebra, geometry and trigonometry.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**MATH 100 Fundamentals of Mathematics 3.0 Credits**

Course covers properties of real numbers, algebraic expressions, rational expressions, linear and quadratic functions and graphs. This course is intended to give students the background needed to enroll in MATH 101.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Can enroll if classification is Freshman or Sophomore .

**Corequisite**: EXAM 082

**MATH 101 Introduction to Analysis I 4.0 Credits**

Covers linear, quadratic, exponential, and logarithmic functions; systems of linear equations; elementary linear programming; matrix algebra; inverse; and mathematics of finance.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**APEM 061 or MATH 100 [Min Grade: D]

**Corequisite**: EXAM 080

**MATH 102 Introduction to Analysis II 4.0 Credits**

Covers limits, continuity, derivatives, indefinite and definite integrals, and applications.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 101 [Min Grade: D]

**Corequisite**: EXAM 080

**MATH 107 Probability and Statistics for Liberal Arts 3.0 Credits**

Probability and statistics in everyday life. The pitfalls of interpreting statistical data. A basic introduction to probability, chance, and gambling. Examples include coin-tossing, dice and roulette wheels.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 100 [Min Grade: D] or APEM 060

**MATH 108 Mathematics for Nursing Professionals 3.0 Credits**

Math foundations needed in the calculation of dosages and solutions of medications. Topics include systems of measurement and calculating dosages involving tablets, capsules, liquids, and powders.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**APEN 070 or MATH 100 [Min Grade: D]

**MATH 110 Precalculus 3.0 Credits**

Reviews topics from algebra, geometry, and trigonometry essential for the study of calculus. For students planning to take Calculus I.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Can enroll if classification is Freshman or Sophomore .

**Corequisite**: EXAM 082

**MATH 119 Mathematical Foundations for Design 4.0 Credits**

This course serves as an introduction to the mathematical concepts and tools most useful to students majoring in the Design Arts. Topics include functions, graphs, plane and fractal geometry, trigonometry, polar coordinates, and elementary topology.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Can enroll if classification is Freshman or Sophomore .

**Corequisite**: EXAM 080

**MATH 121 Calculus I 4.0 Credits**

Functions, limits and continuity, derivatives, trancendental functions, and applications.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Can enroll if classification is Freshman or Sophomore .

**Prerequisites:**APC 070 or APC2 070 or MATH 110 [Min Grade: D]

**Corequisite**: EXAM 080

**MATH 122 Calculus II 4.0 Credits**

Definite integrals, Fundamental Theorem of Calculus, integration techniques, applications of integration, numerical integration and differential equations.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 121 [Min Grade: D]

**Corequisite**: EXAM 080

**MATH 123 Calculus III 4.0 Credits**

Differential equations, Taylor's theorem, sequence and series, convergence, power series.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 122 [Min Grade: D]

**Corequisite**: EXAM 080

**MATH 180 Discrete Computational Structures 4.0 Credits**

Covers basic concepts of discrete mathematics that are important to computing, including elementary set theory, recurrence relations, and graph theory.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 102 [Min Grade: D] or MATH 121 [Min Grade: D]

**MATH 181 Mathematical Analysis I 3.0 Credits**

Covers set theory, coordinate systems and graphs, functions, linear programming (geometric approach), matrices and linear systems, and linear programming (algebraic approach). Required for architecture, business administration, and construction management students. Non-credit for engineering and science students. Fall, Winter.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**MATH 182 Mathematical Analysis II 3.0 Credits**

Covers counting techniques, probability, statistics, and probability applications. Non-credit for engineering and science students. All terms.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 181 [Min Grade: D]

**MATH 183 Mathematical Analysis III 3.0 Credits**

Covers limits, rates of change, derivatives, applications of differentiation, exponential and logarithmic functions, integrals, techniques of integration, applications of integration. Non-credit for engineering and science students. All terms.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 182 [Min Grade: D]

**MATH 200 Multivariate Calculus 4.0 Credits**

Vectors, curves, partial derivatives, gradient, constrained optimization, coordinate system, multiple integrals, and applications.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 122 [Min Grade: D]

**Corequisite**: EXAM 080

**MATH 201 Linear Algebra 4.0 Credits**

Systems of linear equations, matrix algebra, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality, diagonalization, applications.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 121 [Min Grade: D]

**Corequisite**: EXAM 081

**MATH 205 Survey of Geometry 3.0 Credits**

Axiomatic approach to geometry: plane geometry, transformational geometrics, and an introduction to classical non-Euclidean geometries. Includes experimental approaches using appropriate software tools.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 201 [Min Grade: D]

**MATH 210 Differential Equations 4.0 Credits**

Covers solution methods and properties for scalar and vector differential equations. Topics include linear and nonlinear equations, numerical methods, partial differential equations, separation of variables, and transform methods.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 200 [Min Grade: D] and MATH 201 [Min Grade: D]

**MATH 220 Introduction to Mathematical Reasoning 3.0 Credits**

A transition course that develops the reasoning skills necessary for later courses. Emphasizes writing and presentation skills. Topics taken from set theory, logic, induction, relations, functions, and properties of the real number system.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**MATH 221 Discrete Mathematics 3.0 Credits**

Elementary set theory, combinatorics, elementary number theory, graphs, and special topics chosen from formal language theory, graph algorithms, coding theory, and other applications.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 220 [Min Grade: D] or CS 270 [Min Grade: D] or ECE 200 [Min Grade: D]

**Corequisite**: EXAM 081

**MATH 235 Math Competition Problem Solving Seminar 0.5-4.0 Credits**

Problems from math competitions (such as the Putnam exam) are solved by students in this course.This course may be repeated four times for credit as topics vary.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Can be repeated 4 times for NaN credits

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 200 [Min Grade: D]

**MATH 238 History of Mathematics 3.0 Credits**

This course explores the history of mathematical concepts. Both the people involved and the environment in which the developments took place will be studied. Mathematics from the time of Babylonia to the present will be discussed. The presentation will take a thematic approach, which may vary each term.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**MATH 239 Mathematics for the Life Sciences 4.0 Credits**

A broad survey of mathematical topics that are fundamental for application in the life science: multivariate calculus, differential equations, elementary probability. Emphasis on application.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 102 [Min Grade: D]

**MATH 261 Linear Algebra 3.0 Credits**

Covers matrix arithmetic systems of linear equations, including vector spaces, coordinate systems, determinants, characteristic value problems, and Euclidean spaces, and application to quadratic forms and linear differential equations. Problems from engineering and science will be solved using applications such as MATLAB during the lab.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Can enroll if classification is Freshman.

**Prerequisites:**MATH 122 [Min Grade: D]

**MATH 262 Differential Equations 3.0 Credits**

Covers solutions of first-order equations, undetermined coefficient and variation of parameter methods of solution of higher order linear equations, systems of equations, and Laplace transform. Problems from engineering and science will be solved using applications such as MATLAB during the lab.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 261 [Min Grade: D]

**MATH 279 Special Topics in Mathematics 12.0 Credits**

Covers topics in pure or applied mathematics. Different topics may be considered in different quarters.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Can be repeated multiple times for credit

**Restrictions:**Cannot enroll if classification is Freshman

**MATH 285 Differential Equations II 3.0 Credits**

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 210 [Min Grade: D]

**MATH 286 Applied Differential Equations 3.0 Credits**

Reviews basic methods, including applications to electric circuits, chemical mixtures, mechanics, and motion problems. Introduces partial differential equations. Spring. Alternate years.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 285 [Min Grade: D]

**MATH 291 Complex and Vector Analysis for Engineers 4.0 Credits**

Complex and Vector Analysis for Engineers. Covers gradient, divergence, and curl; integral theorems curvilinear coordinates, complex differentiation and integration, Cauchy's Theorem, power series, residues and applications.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 200 [Min Grade: D] and PHYS 102 [Min Grade: D]

**MATH 300 Numerical Analysis I 4.0 Credits**

The course covers polynomial and trigonometric interpolation, splines, numerical linear algebra, numerical quadrature, solutions of nonlinear equations, and nonlinear optimization. The course emphasizes computational solutions.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 200 [Min Grade: D] and MATH 201 [Min Grade: D] and (CS 171 [Min Grade: D] or CS 123 [Min Grade: D])

**MATH 301 Numerical Analysis II 3.0 Credits**

A continuation of MATH 300. This course focuses on time dependent problems. It includes numerical solution of ordinary differential equation, the heat and wave equations, and moving interfaces. The discussed techniques include implicit schemes or ODEs, finite differences, spectral methods and the level set method.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 300 [Min Grade: D]

**MATH 305 Introduction to Optimization Theory 4.0 Credits**

Provides a broad survey of mathematical techniques in optimization theory used in operations research and management science. Includes topics selected from the following categories: linear programming, integer programming, network flows, and nonlinear programming.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 201 [Min Grade: D]

**MATH 310 Probability and Statistics 4.0 Credits**

Not open to mathematics or computer science majors. Covers probability, probability distribution of discrete and continuous random variables, moment-generating functions, distribution of sample statistics, estimation and statistical tests, tests for goodness of fit, and regression analysis.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if major is CS or major is MATH or classification is Freshman

**Prerequisites:**MATH 200 [Min Grade: D]

**MATH 311 Probability and Statistics I 4.0 Credits**

Covers sample spaces, axioms and theorems of elementary probability, random variables, distributions and expectation, mean, variance, moment-generating functions, Chebyshev's inequality, law of large numbers, and central limit theorem.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 200 [Min Grade: D]

**Corequisite**: EXAM 081

**MATH 312 Probability and Statistics II 4.0 Credits**

Covers estimation, consistency, unbiasedness, maximum likelihood, confidence intervals, hypothesis testing, Type I and Type II errors, Neyman Pearson lemma, likelihood ratio tests, and tests for means and variances.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 311 [Min Grade: D]

**Corequisite**: EXAM 081

**MATH 316 Mathematical Applications of Symbolic Software 3.0 Credits**

Mathematical Applications of Symbolic Software. Topics from calculus are investigated via complex problems requiring the use of symbolic mathematical software, primarily Maple. Numerical, graphical, and algebraic approaches are integrated. Limits, derivatives, root-finding, integration, and infinite series are explored in this context.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 123 [Min Grade: D] and MATH 200 [Min Grade: D]

**MATH 318 [WI] Mathematical Applications of Statistical Software 3.0 Credits**

Mathematical Applications of Statistical Software. Applications of modern statistical technologies and software, such as SAS, are used to describe and analyze data. Some topics covered are data management, collecting data, inferences for single and multiple population means, proportions count data, regression, correlation and nonparametric statistical methods. This is a writing intensive course.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 310 [Min Grade: D] or MATH 312 [Min Grade: D]

**MATH 319 Techniques of Data Analysis 4.0 Credits**

An applied course that considers the acquisition, analysis, visualization, and presentation of data. Emphasizes computation.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 318 [Min Grade: D]

**MATH 320 Actuarial Mathematics 3.0 Credits**

Covers probability in a risk management context. Univariate probability distribution including binomial, negative binomial, Poisson, uniform, exponential, normal, lognormal, Pareto, and Weibull distributions. Multivariate distributions including conditional and marginal probability distributions, joint moment generating functions, probability and moments for linear combinations of independent random variables and related topics.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 311 [Min Grade: D]

**MATH 321 Vector Calculus 4.0 Credits**

Covers vector algebra; gradient, divergence, curl, and curvilinear coordinates; Green's theorem, divergence theorem, and Stokes' theorem; and applications.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 200 [Min Grade: D] and MATH 201 [Min Grade: D]

**MATH 322 Complex Variables 4.0 Credits**

Introduces functions of one complex variable. Topics include the basic properties of analytic functions, power series, integration, residues and poles, and conformal mapping with applications.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 210 [Min Grade: D]

**MATH 323 Partial Differential Equations 4.0 Credits**

Covers basic concepts and solution techniques for the standard partial differential equations of mathematical physics.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 210 [Min Grade: D]

**MATH 331 Abstract Algebra I 4.0 Credits**

Covers theory of groups, homomorphism and isomorphism, theory of rings, integral domains, ideals, unique factorization, and theory of fields.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**(MATH 220 [Min Grade: C-] or CS 270 [Min Grade: C-]) and (MATH 201 [Min Grade: D] or MATH 261 [Min Grade: D] or ENGR 231 [Min Grade: D])

**MATH 332 Abstract Algebra II 3.0 Credits**

Covers further topics in abstract algebra, including canonical decomposition of linear transformation, bilinear forms, multilinear algebra and determinants, finite fields, and selected short subjects.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 331 [Min Grade: C-]

**MATH 382 Advanced Calculus 3.0 Credits**

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**MATH 387 Linear Algebra II 3.0 Credits**

Covers linear transformations, including kernel and range; eigenvalues and eigenvectors; diagonalization of symmetric matrices; and application to differential equations, quadratic forms, and Markov chains. Fall.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**or MATH 201 [Min Grade: D], MATH 261 [Min Grade: D] or MATH 201 [Min Grade: D]

**MATH 401 Elements of Modern Analysis I 3.0 Credits**

Covers the real number system, elementary topology, limits, infinite series, continuity, derivatives, and the Riemann integral.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**(MATH 220 [Min Grade: C-] or CS 270 [Min Grade: C-]) and (MATH 201 [Min Grade: D] or MATH 261 [Min Grade: D] or ENGR 231 [Min Grade: D]) and MATH 200 [Min Grade: D]

**MATH 402 Elements of Modern Analysis II 3.0 Credits**

Covers continuation of integration theory, improper integrals, sequences and series, power series, and uniform convergence.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 401 [Min Grade: C-]

**MATH 410 Scientific Data Analysis I 3.0 Credits**

Fundamental principles and applications of statistics for scientific data analysis. Topics include data exploration, principles of probability distributions, Central Limit Theorem, hypothesis testing, z, t and F tests, one-way analysis of variance, linear regression, and contingency table analysis. Programming statistical applications in R will be included.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 122 [Min Grade: D] or MATH 239 [Min Grade: D]

**MATH 411 Scientific Data Analysis II 3.0 Credits**

Scientific data analysis and experimental design. Topics include multiple regression and model selection, nonlinear and logistic regression, analysis of covariance, multi-factor analysis of variance, nested, factorial and repeated measures experimental designs, random effects, and introduction to bootstrap methods and randomization tests. Programming statistical applications in R will be included.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 410 [Min Grade: C-]

**MATH 422 Introduction to Topology 4.0 Credits**

Covers topological space, metric spaces, function, continuity, compactness, and connectedness.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 200 [Min Grade: D] or MATH 201 [Min Grade: D]

**MATH 449 Mathematical Finance 3.0 Credits**

This course is an introduction to the mathematics of finance. The main topics include: fixed income mathematics (duration, convexity, compounding conventions, immunization of bond portfolios, yield curve stripping), foundations of the arbitrage theory (pricing of futures and forwards, swaps, put/call parity) and introduction to stochastic derivative pricing (Black-Scholes and beyond).

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 311 [Min Grade: D]

**MATH 450 Introduction to Graph Theory 3.0 Credits**

Introduction to Graph Theory. Topics covered include paths and cycles, Eulerian graphs, Hamiltonian graphs, trees, matching, coloring, planarity, and some additional topics in special graphs such as interval graphs.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 201 [Min Grade: D] and MATH 221 [Min Grade: D]

**MATH 475 Cryptography 3.0 Credits**

Classic cryptosystems, elementary number theory, RSA, ElGamal, discrete logarithms, digital signatures, plus a special topic selected from elliptic curves, information theory, and quantum cryptography.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Prerequisites:**MATH 201 [Min Grade: D] and MATH 311 [Min Grade: D]

**MATH 480 Special Topics in Mathematics 12.0 Credits**

Covers topics in Mathematics of interest to students or faculty. Different topics may be considered during different quarters.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Can be repeated multiple times for credit

**MATH 483 Discrete Event Simulation 3.0 Credits**

Covers system simulation, Monte Carlo methods, discrete event modeling techniques, queuing models, programming considerations, statistical definitions and concepts, random number generation, output analysis, and design of computer experiments. Spring.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 385 [Min Grade: D]

**MATH 489 Tensor Analysis 3.0 Credits**

Covers tensor algebra, including coordinate transformations, fundamental quadratic form, covariant and contravariant tensors, Riemannian metric, and applications. Elective. Spring. Alternate years.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Not repeatable for credit

**Restrictions:**Cannot enroll if classification is Freshman

**Prerequisites:**MATH 381 [Min Grade: D]

**MATH 497 Independent Study in Mathematics 0.5-12.0 Credits**

Provides supervised study of selected topics in mathematics.

**College/Department:**College of Arts and Sciences

**Repeat Status:**Can be repeated multiple times for credit

**Restrictions:**Cannot enroll if classification is Freshman

**MATH 498 Special Topics 12.0 Credits**

**College/Department:**College of Arts and Sciences

**Repeat Status:**Can be repeated multiple times for credit

**MATH 499 Independent Study in Mathematics 6.0 Credits**

**College/Department:**College of Arts and Sciences

**Repeat Status:**Can be repeated multiple times for credit

## Mathematics Faculty

*(Duke University)*

*Associate Department Head of the Mathematics Department*. Associate Professor. Applied analysis and computing for systems of nonlinear partial differential equations, especially free-surface problems in fluid dynamics.

*(Drexel University)*. Assistant Teaching Professor.

*(University of California at Berkeley)*. Assistant Professor. Algebraic combinatorics, representation theory, and complexity theory.

*(University of Pennsylvania)*

*Interim Associate Head of the Mathematics Department*. Professor. Functional analysis, C*-algebras and the theory of group representations.

*(University of Miami)*. Assistant Professor. Homological mirror symmetry, Landau-Ginzburg models, algebraic geometry, symplectic geometry.

*(University of Colorado at Boulder)*. Assistant Teaching Professor. Number theory specializing in modular forms and function fields.

*(Case Western Reserve University)*. Associate Teaching Professor. Applied mathematics.

*(Drexel University)*. Associate Teaching Professor. Math foundations of engineering.

*(Drexel University)*. Assistant Teaching Professor. Discrete mathematics and automata theory.

*(Drexel University)*. Assistant Teaching Professor.

*(Massachusetts Institute of Technology)*. Associate Professor. Intersection of physics, engineering, applied mathematics and computational science.

*(University of California at Berkeley)*. Assistant Teaching Professor. Function theory and operator theory, harmonic analysis, matrix theory.

*(University of Pittsburgh)*. Associate Professor. Biomathematics, dynamical systems, ordinary and partial differential equations and math education.

*(University of Pennsylvania)*. Professor. Geometry and optical design.

*(Warsaw University)*. Professor. Probability theory and its applications to analysis, combinatorics, wavelets, and the analysis of algorithms.

*(Drexel University)*. Assistant Teaching Professor.

*(Kharkov National University)*. Associate Professor. Operator theory, systems theory, complex analysis, C*-algebras and harmonic analysis.

*(University of Utah)*. Assistant Teaching Professor. Electromagnetic wave propagation in composite media, optimization and inverse problem.

*(York University)*. Assistant Teaching Professor. Algebraic combinatorics.

*(Boston University)*. Associate Professor. Ordinary and partial differential equations, mathematical neuroscience.

*(Ben Gurion University, Israel)*. Assistant Teaching Professor. System/operator theory, scattering theory, differential rings theory.

*(University of California, San Diego)*

*Undergraduate Advisor*. Professor. Algebraic combinatorics.

*(Rutgers University)*

*Associate Head of the Mathematics Department*. Professor. Partial differential equations and numerical analysis, including homogenization theory, numerical methods for problems with rough coefficients, and inverse problems.

*(Drexel University)*. Associate Teaching Professor.

*(Omsk State University)*. Associate Teaching Professor. Math education.

*(Drexel University)*. Instructor.

*(University of California at Berkeley)*. Associate Professor. Applied mathematics, numerical analysis, symbolic computation, differential geometry, mathematical physics.

*(University of California at Berkeley)*. Associate Professor. Applied mathematics, computed tomography, numerical analysis of function reconstruction, signal processing, combinatorics.

*(Drexel University)*. Associate Teaching Professor.

*(Drexel University)*. Teaching Professor. Probability and statistics.

*(University of Pennsylvania)*. Professor. Probabilistic combinatorics, asymptotic enumeration.

*(Rutgers University)*. Associate Professor. Discrete optimization, combinatorics, operations research, graph theory and its application in molecular biology, social sciences and communication networks, biostatistics.

*(Columbia University)*. Assistant Professor. Partial differential equations, scientific computing and applied mathematics.

*(West Chester University)*. Assistant Teaching Professor.

*(Courant Institute, New York University)*. Professor. Homotopy theory, operad theory, quantum mechanics, quantum computing.

*(Boston University)*. Assistant Teaching Professor.

*(Harvard University)*. Assistant Teaching Professor. Applied statistics, data analysis, calculus, discrete mathematics, biostatistics.

*(Columbia University)*. Instructor.

*(Penn State University)*. Assistant Teaching Professor.

*(Vrije Universiteit, Amsterdam)*

*Department Head, Department of Mathematics*. Professor. Matrix and operator theory, systems theory, signal and image processing, and harmonic analysis.

*(Boston University)*

*Graduate Advisor*. Associate Professor. Partial differential equations, specifically nonlinear waves and their interactions.

*(Cornell University)*. Assistant Teaching Professor. Dynamical systems, neurodynamics.

*(Stanford University)*. Professor. Multiscale mathematics, wavelets, applied harmonic analysis, subdivision algorithms, nonlinear analysis, applied differential geometry and data analysis.

## Emeritus Faculty

*(University of Washington)*. Professor Emeritus. Functional analysis, wavelets, abstract harmonic analysis, the theory of group representations.

*(University of Pennsylvania)*. Professor Emeritus. Functional analysis, C*-algebras and group representations, computer science.

*(Temple University)*

*Dean Emeritus*. Professor Emeritus. Mathematics education, curriculum and instruction, minority engineering education.

*(Ohio State University)*. Associate Professor Emeritus. Number theory, approximation theory and special functions, combinatorics, asymptotic analysis.

*(University of Pennsylvania)*. Professor Emeritus. Lie algebras; theory, applications, and computational techniques; operations research.

*(University of California at Davis)*. Professor Emeritus. Probability and statistics, biostatistics, epidemiology, mathematical demography, data analysis, computer-intensive methods.

*(Courant Institute, New York University)*. Professor Emeritus. Applied mathematics, scattering theory, mathematical modeling in biological sciences, solar-collection systems.

*(University of Edinburgh)*. Professor Emeritus. Applied mathematics, special factors, approximation theory, numerical techniques, asymptotic analysis.

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