Mathematics Major

Program Director: Larry Washington, Ph.D. 

The program in Mathematics leads to a degree of Bachelor of Science in Mathematics and offers students training in preparation for graduate work, teaching, and positions in government or industry.  Mathematical training is integrated with computer use in several courses.  Because a strong mathematical background is important in many fields, over half of UMCP Mathematics majors are double majors.  Additional information on these topics and mathematics is available from the departmental website.

Placement in Courses

The Department of Mathematics has a large offering to accommodate a great variety of background, interests, and abilities. The department permits students to take any course for which they have the appropriate background, regardless of formal course work. For example, students with a high school calculus course may be permitted to begin in the middle of the calculus sequence even if they do not have advanced standing. Students may obtain undergraduate credit for mathematics courses in any of the following ways: passing the appropriate CEEB Advanced Placement Examination, passing standardized CLEP examinations, and through the department's credit-by-examinations. Students are urged to consult with advisors from the Department of Mathematics to assist with proper placements.

Program Objectives

The Department of Mathematics educates its majors in a broad range of modern mathematics while instilling in them a strong ability to solve problems, apply mathematics to other areas, and create rigorous mathematical arguments. The program prepares the majors to further their mathematical education in graduate school, or to teach at the secondary school level, or to work in government or business.

Program Learning Outcomes

  1. Students will acquire problem-solving skills in a broad range of significant mathematics.
  2. Students will gain an understanding of what constitutes mathematical thinking, including the ability to produce and judge the validity of rigorous mathematical arguments.
  3. Students will be able to communicate mathematical ideas and arguments.
  4. Students will be prepared to use mathematics in their future endeavors, not only in the discipline of mathematics, but also in other disciplines.

Statistics and Probability and Applied Mathematics

Courses in statistics and probability, and applied mathematics are offered by the Department of Mathematics.  These courses are open to non-majors as well as majors, and carry credit in mathematics. Students wishing to concentrate in the above may do so by choosing an appropriate program under the Department of Mathematics.

There are four tracks for the major:  the traditional track, the applied mathematics track, the secondary education track, and the statistics track. The secondary education track is for students seeking to become certified to teach mathematics at the secondary level. Each mathematics major must complete each required course with a grade of C- or better and with an overall major GPA of 2.0.

Traditional Track

Course Title Credits
Introductory Sequence 1
MATH140Calculus I4
MATH141Calculus II4
MATH240Introduction to Linear Algebra4
MATH241Calculus III4
MATH310Introduction to Mathematical Proof3
Select one of the following:3
Differential Equations for Scientists and Engineers
Differential Geometry of Curves and Surfaces I
Partial Differential Equations
MATH/AMSC/STAT Courses
Select eight courses of 400-level or higher; must include: 2
MATH410Advanced Calculus I3
Select one of the following:3
Applications of Linear Algebra
Introduction to Abstract Algebra
Linear Algebra
Select one of the following:3
Computational Methods
Introduction to Numerical Analysis I
Any 400-level STAT course other than STAT4643
Select depth requirement; a one year sequence chosen from the following:3-6
Advanced Calculus I
and Advanced Calculus II
Introduction to Abstract Algebra
and Field Theory
Introduction to Abstract Algebra
and Linear Algebra
Introduction to Probability Theory
and Theory and Methods of Statistics
Select electives: 400-level MATH/AMSC/STAT course 3, 46-9
Computer Programming Requirement
Select one of the following:3-4
Introduction to C Programming
Object-Oriented Programming I
Object-Oriented Programming II
Computing Fundamentals for Engineers
Intermediate Programming Concepts for Engineers
Introduction to Scientific Programming
Supporting three-course sequence 5
Select one of eight sequences 9-13
Sequence One (11 credits)
General Physics: Mechanics and Particle Dynamics
General Physics: Electricity, Magnetism and Thermodynamics
and General Physics: Mechanics, Vibrations, Waves, Heat (Laboratory)
General Physics: Waves, Optics, Relativity and Modern Physics
and General Physics: Electrodynamics, Light, Relativity and Modern Physics (Laboratory)
Sequence Two (9 credits)
Introductory Physics: Mechanics
Introductory Physics: Fields
Introductory Physics: Oscillations and Waves
Sequence Three (9 credits)
Mechanics I
General Physics: Mechanics and Particle Dynamics
Mechanics II
Sequence Four (12 credits)
Object-Oriented Programming I
Object-Oriented Programming II
Introduction to Computer Systems
Sequence Five (13 credits)
Principles of General Chemistry
and Introduction to Laboratory Practices and Research in the Chemical Sciences
Principles of Organic Chemistry I
Principles of Organic Chemistry II
Sequence Six (12 credits)
Chemistry I - Fundamentals of General Chemistry
and General Chemistry I Laboratory
Organic Chemistry I
and Organic Chemistry Laboratory I
Organic Chemistry II
and Organic Chemistry Laboratory II
Sequence Seven (11 credits)
Principles of Microeconomics
Principles of Macroeconomics
Intermediate Macroeconomic Theory and Policy
Intermediate Microeconomic Theory & Policy
OR
Intermediate Macroeconomic Analysis
Intermediate Microeconomic Analysis
Sequence Eight (9 credits)
Principles of Accounting I
Principles of Accounting II
Business Finance
Total Credits55-66
1

Or honors sequence: MATH340-MATH341.Completion of MATH340 satisfies the requirement for MATH241; completion of MATH340-MATH341 satisfies the requirement for MATH240-MATH241-MATH246.

2

At least four courses must be taken at College Park.

3

400 level courses. Students with a strong interest in applied mathematics may, with the approval of the Undergraduate Office, substitute two courses (with strong mathematics content) from outside the Mathematics Department for one upper-level elective course.

4

May not include:  MATH461, MATH478, MATH480-MATH484, STAT464

5

Intended to broaden the student's mathematical experience. (Other sequences might be approved by the Undergraduate Office but they would have to make use of mathematical ideas, comparable to the sequences on this list.)

Applied Mathematics Track

Course Title Credits
Introductory Sequence 1
MATH140Calculus I4
MATH141Calculus II4
MATH240Introduction to Linear Algebra4
MATH241Calculus III4
MATH310Introduction to Mathematical Proof3
Select one of the following:3
Differential Equations for Scientists and Engineers
Differential Geometry of Curves and Surfaces I
Partial Differential Equations
MATH/AMSC/STAT Courses
Select eight 400-level or higher; must include: 2
MATH410Advanced Calculus I3
STAT410Introduction to Probability Theory3
STAT4XXOne additional STAT course other than STAT400, STAT410, STAT4643
MATH401Applications of Linear Algebra3
or MATH405 Linear Algebra
AMSC460Computational Methods3
or AMSC466 Introduction to Numerical Analysis I
Select one of the following:3
Applied Harmonic Analysis: An Introduction to Signal Processing
Mathematical Modeling
Introduction to the Mathematics of Finance
Geometry for Computer Applications
Introduction to Dynamics and Chaos
Cryptography
Partial Differential Equations
Complex Variables
Transform Methods
Combinatorics and Graph Theory
Select depth requirement; a one year sequence chosen from the following:3
Advanced Calculus I
and Advanced Calculus II
Applied Harmonic Analysis: An Introduction to Signal Processing
and Transform Methods
Partial Differential Equations
and Complex Variables
Introduction to Probability Theory
and Theory and Methods of Statistics
Select electives: 400-level MATH/AMSC/STAT course 3
Computer Programming Requirement
Select one of the following:
Introduction to C Programming
Object-Oriented Programming I
Object-Oriented Programming II
Computing Fundamentals for Engineers
Intermediate Programming Concepts for Engineers
Introduction to Scientific Programming
Supporting Three-course Sequence 4
Select one of twelve sequences9-13
Sequence One (11 credits)
General Physics: Mechanics and Particle Dynamics
General Physics: Electricity, Magnetism and Thermodynamics
and General Physics: Mechanics, Vibrations, Waves, Heat (Laboratory)
General Physics: Waves, Optics, Relativity and Modern Physics
and General Physics: Electrodynamics, Light, Relativity and Modern Physics (Laboratory)
Sequence Two (9 credits)
Introductory Physics: Mechanics
Introductory Physics: Fields
Introductory Physics: Oscillations and Waves
Sequence Three (9 credits)
Mechanics I
General Physics: Mechanics and Particle Dynamics
Mechanics II
Sequence Four (12 credits)
Object-Oriented Programming I
Object-Oriented Programming II
Introduction to Computer Systems
Sequence Five (13 credits)
Principles of General Chemistry
and Introduction to Laboratory Practices and Research in the Chemical Sciences
Principles of Organic Chemistry I
Principles of Organic Chemistry II
Sequence Six (12 credits)
Chemistry I - Fundamentals of General Chemistry
and General Chemistry I Laboratory
Organic Chemistry I
and Organic Chemistry Laboratory I
Organic Chemistry II
and Organic Chemistry Laboratory II
Sequence Seven (11 credits)
Principles of Microeconomics
Principles of Macroeconomics
Intermediate Macroeconomic Theory and Policy
Intermediate Microeconomic Theory & Policy
OR
Intermediate Macroeconomic Analysis
Intermediate Microeconomic Analysis
Sequence Eight (9 credits)
Principles of Accounting I
Principles of Accounting II
Business Finance
Sequence Nine (12-13 credits)
Principles of Molecular & Cellular Biology
and Principles of Molecular & Cellular Biology Laboratory
Principles of Ecology and Evolution
and Principles of Ecology and Evolution Lab
Chemistry I - Fundamentals of General Chemistry
and General Chemistry I Laboratory
OR
Principles of General Chemistry
and Introduction to Laboratory Practices and Research in the Chemical Sciences
Sequence Ten (10 credits)
Introductory Astrophysics - Solar System
Introductory Astrophysics II - Stars and Beyond 5
General Physics: Mechanics and Particle Dynamics
Introductory Physics: Mechanics
Sequence Eleven (12 credits)
Physical Geology
Select Two From:
Mineralogy
Geomorphology
Structural Geology
Introduction to the Blue Ocean
Sequence Twelve (10 credits)
Weather and Climate
and Weather and Climate Laboratory
Two additional 400-level AOSC courses
Total Credits52-56
1

Or honors sequence: MATH340-MATH341.Completion of MATH340 satisfies the requirement for MATH241; completion of MATH340-MATH341 satisfies the requirement for MATH240-MATH241-MATH246.

2

At least four courses must be taken at College Park.

3

400 level courses.  May not include:  MATH461MATH478MATH480-MATH484STAT464

4

Intended to broaden the student's mathematical experience. (Other sequences might be approved by the Undergraduate Office but they would have to make use of mathematical ideas, comparable to the sequences on this list.

5

ASTR121 is restricted to Astronomy majors, but may be open to Mathematics majors if space is available. Consequently, Mathematics majors are not guaranteed a seat in this course. Contact the Astronomy department for more information.

Secondary Education Track    

Course Title Credits
Introductory Sequence 1
MATH140Calculus I4
MATH141Calculus II4
MATH240Introduction to Linear Algebra4
MATH241Calculus III4
MATH310Introduction to Mathematical Proof3
Select one of the following:3-4
Differential Equations for Scientists and Engineers
Multivariable Calculus, Linear Algebra, Differential Equations II (Honors)
Applications of Linear Algebra
Mathematical Modeling
Introduction to Dynamics and Chaos
Partial Differential Equations
Computational Methods
Introduction to Numerical Analysis I
MATH/AMSC/STAT Courses 2
Select seven courses at the 400-level or higher, must include:
MATH410Advanced Calculus I3
MATH430Euclidean and Non-Euclidean Geometries3
MATH402Algebraic Structures3
or MATH403 Introduction to Abstract Algebra
STAT400Applied Probability and Statistics I3
or STAT410 Introduction to Probability Theory
Select one of the following:3
Introduction to Number Theory
Elementary Mathematical Logic
Axiomatic Set Theory
Cryptography
Combinatorics and Graph Theory
Select electives: 400-level MATH/AMSC/STAT course 3
Computer Programming Requirement
Select one of the following:3-4
Introduction to C Programming
Object-Oriented Programming I
Object-Oriented Programming II
Computing Fundamentals for Engineers
Intermediate Programming Concepts for Engineers
Introduction to Scientific Programming
Education Requirements 4
TLPL478Professional Seminar in Education (TLPL478D: Professional Seminar in Education: Mathematics)1
TLPL488Special Topics in Education (TLPL488B: Teaching Academically, Culturally and Linguistically Diverse Students in Secondary Education)2
TLPL489Internship in Education (TLPL489D: Internship in Education: Mathematics)12
Supporting Sequence 5
Select one of six sequences7-8
Sequence One (8 credits)
Chemistry I - Fundamentals of General Chemistry
and General Chemistry I Laboratory
Organic Chemistry I
and Organic Chemistry Laboratory I
Sequence Two (7 credits)
General Physics: Mechanics and Particle Dynamics
General Physics: Electricity, Magnetism and Thermodynamics
and General Physics: Mechanics, Vibrations, Waves, Heat (Laboratory)
Sequence Three (8 credits)
Principles of Molecular & Cellular Biology
and Principles of Molecular & Cellular Biology Laboratory
Principles of Ecology and Evolution
and Principles of Ecology and Evolution Lab
Sequence Four (7 credits)
Introductory Astrophysics - Solar System
Introductory Astrophysics II - Stars and Beyond
Sequence Five (7-8 credits)
Physical Geology
and Physical Geology Laboratory
Mineralogy
Geomorphology
Structural Geology
Introduction to the Blue Ocean
Sequence Six (7 credits)
Weather and Climate
and Weather and Climate Laboratory
AOSC4xx Any 400 level AOSC course
Total Credits62-65
1

Or honors sequence: MATH340-MATH341.Completion of MATH340 satisfies the requirement for MATH241; completion of MATH340-MATH341 satisfies the requirement for MATH240-MATH241-MATH246.

2

At least four courses must be taken at College Park.

3

May not include:  MATH461,MATH478, MATH480-MATH484, or STAT464

4

The student-teaching courses have further prerequisites in the College of Education. In order to take these courses the student must be admitted into the College of Education. A student in the secondary education track of the mathematics major would normally be expected to receive a double major in Mathematics and Mathematics Education.

5

These are intended to broaden the student's mathematical experience. (Other sequences might be approved by the Undergraduate Office but they would have to make use of mathematical ideas, comparable to the sequences on this list.

Statistics Track 

Course Title Credits
Introductory Sequence 1
MATH140Calculus I4
MATH141Calculus II4
MATH240Introduction to Linear Algebra4
MATH241Calculus III4
MATH310Introduction to Mathematical Proof3
Select one of the following:3
Differential Equations for Scientists and Engineers
Differential Geometry of Curves and Surfaces I
Partial Differential Equations
MATH/AMSC/STAT Courses 2
Select eight courses, must include:
MATH410Advanced Calculus I3
STAT410Introduction to Probability Theory3
STAT430Introduction to Statistical Computing with SAS3
AMSC460Computational Methods3
or AMSC466 Introduction to Numerical Analysis I
MATH401Applications of Linear Algebra3
or MATH405 Linear Algebra
STAT401Applied Probability and Statistics II3
or STAT420 Theory and Methods of Statistics
Select two of the following:6
STAT4xx
Any 400-level or higher STAT courses 3
Advanced Calculus II
Mathematical Modeling
Introduction to the Mathematics of Finance
Transform Methods
Computer Programming Requirement
Select one of the following:3-4
Introduction to C Programming
Object-Oriented Programming I
Object-Oriented Programming II
Computing Fundamentals for Engineers
Intermediate Programming Concepts for Engineers
Introduction to Scientific Programming
Supporting Three-course Sequence 4
Select one of eight sequences9-13
Sequence One (11 credits)
General Physics: Mechanics and Particle Dynamics
General Physics: Electricity, Magnetism and Thermodynamics
and General Physics: Mechanics, Vibrations, Waves, Heat (Laboratory)
General Physics: Waves, Optics, Relativity and Modern Physics
and General Physics: Electrodynamics, Light, Relativity and Modern Physics (Laboratory)
Sequence Two (9 credits)
Introductory Physics: Mechanics
Introductory Physics: Fields
Introductory Physics: Oscillations and Waves
Sequence Three (9 credits)
Mechanics I
General Physics: Mechanics and Particle Dynamics
Mechanics II
Sequence Four (12 credits)
Object-Oriented Programming I
Object-Oriented Programming II
Introduction to Computer Systems
Sequence Five (13 credits)
Principles of General Chemistry
and Introduction to Laboratory Practices and Research in the Chemical Sciences
Principles of Organic Chemistry I
Principles of Organic Chemistry II
Sequence Six (12 credits)
Chemistry I - Fundamentals of General Chemistry
and General Chemistry I Laboratory
Organic Chemistry I
and Organic Chemistry Laboratory I
Organic Chemistry II
and Organic Chemistry Laboratory II
Sequence Seven (11 credits)
Principles of Microeconomics
Principles of Macroeconomics
Intermediate Macroeconomic Theory and Policy
Intermediate Microeconomic Theory & Policy
OR
Intermediate Macroeconomic Analysis
Intermediate Microeconomic Analysis
Sequence Eight (9 credits)
Principles of Accounting I
Principles of Accounting II
Business Finance
Total Credits58-63
1

Or honors sequence: MATH340-MATH341.Completion of MATH340 satisfies the requirement for MATH241; completion of MATH340-MATH341 satisfies the requirement for MATH240-MATH241-MATH246.

2

At least four courses must be taken at College Park.

3

except STAT464

4

Intended to broaden the student's mathematical experience. (Other sequences might be approved by the Undergraduate Office but they would have to make use of mathematical ideas comparable to the sequences on this list.)

Other Requirements for the Major

Areas of Study

Within the Department of Mathematics there are a number of identifiable areas which students can pursue to suit their own goals and interests. They are briefly described below. Note that they do overlap and that students need not confine themselves to one of them.

1. Pure Mathematics

Courses that belong to this area include:

Course Title Credits
MATH402Algebraic Structures3
MATH403Introduction to Abstract Algebra3
MATH404Field Theory3
MATH405Linear Algebra3
MATH406Introduction to Number Theory3
MATH410Advanced Calculus I3
MATH411Advanced Calculus II3
MATH430Euclidean and Non-Euclidean Geometries3
MATH432Introduction to Topology3
MATH436Differential Geometry of Curves and Surfaces I3
MATH437Differential Forms3
MATH445Elementary Mathematical Logic3
MATH452Introduction to Dynamics and Chaos3
MATH456Cryptography3
STAT410Introduction to Probability Theory3
STAT420Theory and Methods of Statistics3
Students preparing for graduate school in mathematics should include:
MATH403Introduction to Abstract Algebra3
MATH405Linear Algebra3
MATH410Advanced Calculus I3
MATH411Advanced Calculus II3
MATH463Complex Variables3
or MATH660 Complex Analysis I
MATH432Introduction to Topology (is also desirable)3
or MATH730 Fundamental Concepts of Topology

Other courses from the above list and graduate courses are also appropriate.

2. Secondary Teaching

In addition to the courses required by the Secondary Education Track, the following courses are particularly suited for students preparing to teach:

Course Title Credits
MATH401Applications of Linear Algebra3
MATH406Introduction to Number Theory3
MATH445Elementary Mathematical Logic3
MATH470Mathematics for Secondary Education3
MATH475Combinatorics and Graph Theory3


Students who are interested in secondary teaching should contact also the College of Education for certification requirements and other information:  www.education.umd.edu/studentinfo.

3. Statistics

For a student with a Bachelor's degree seeking work requiring some statistical background, the minimal program is STAT400-STAT401. To work primarily as a statistician, one should combine STAT400-STAT401 with STAT430 and at least one more statistics course, most suitably, STAT440.   A deeper sequence is STAT410, STAT420, STAT430. This offers a better understanding and wider knowledge of statistics and is a general purpose program (i.e., does not specify one area of application).    For economics applications,

MATH424, STAT400, STAT401, STAT430, STAT440 should be considered. To prepare for graduate work, STAT410 and STAT420 give the best background, with STAT430, STAT440 added at some later stage.

4. Computational Mathematics

There are a number of math courses which emphasize the computational aspects of mathematics including the use of the computer. They are:

Course Title Credits
AMSC460Computational Methods3
AMSC466Introduction to Numerical Analysis I3
MATH431Geometry for Computer Applications3
MATH456Cryptography3
MATH475Combinatorics and Graph Theory3
STAT430Introduction to Statistical Computing with SAS3

Students interested in this area should take the CMSC supporting sequence as soon as possible.

5. Applied Mathematics

The courses that lead most rapidly to applications are the courses listed above in 3 and 4 and

Course Title Credits
MATH401Applications of Linear Algebra3
MATH416Applied Harmonic Analysis: An Introduction to Signal Processing3
MATH420Mathematical Modeling3
MATH452Introduction to Dynamics and Chaos3
MATH462Partial Differential Equations3
MATH464Transform Methods3

A student interested in applied mathematics should obtain, in addition to a solid training in mathematics, a good knowledge of at least one area in which mathematics is currently being applied. Concentration in this area is good preparation for employment in government and industry or for graduate study in applied mathematics.

Click here for roadmaps for graduation plans in the College of Computer, Mathematical, and Natural Sciences.

Additional information on developing a graduation plan can be found on the following pages: