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Undergraduate Catalog 2012-2013

MATHEMATICS (MATH)

College of Computer, Mathematical and Physical Sciences
1117 Mathematics Building, 301-405-5053
www.math.umd.edu
Chair: J. Yorke (Dist Univ Prof, Chair)
Professors: J. Adams, S. Antman (Dist Univ Prof, Assoc Chair APT), R. Balan, J. Benedetto (Dist Teacher Scholar), M. Boyle, P. Brosnan, J. Cohen, D. Dolgopyat, P. Fitzpatrick, G. Forni, M. Freidlin (Dist Univ Prof), H. Glaz, W. Goldman (Dist Teacher Scholar), M. Grillakis, D. Gulick (Assoc Chair, Course Staffing), T. Haines, S. Halperin, D. Hamilton, B. Hunt, P. Jabin, M. Jakobson, A. Kagan (Director of Statistics Program), V. Kaloshin (Brin Chair), B. Kedem, W. Kirwan (Chancellor), D. Kueker, M. Laskowski, C. Levermore, D. Levy (Assoc Chair, Undergraduate Studies), M. Machedon (Assoc Chair, Faculty Affairs), J. Millson, R. Nochetto, S. Novikov (Dist Univ Prof), J. Ren, J. Rosenberg (Davis Prof), J. Schafer, E. Slud, E. Tadmor (Dist Univ Prof, Director of CSCAMM), H. Tamvakis, K. Trivisa (Director of AMSC Program), L. Washington (Assoc Chair, Graduate Studies), R. Wentworth, P. Wolfe, S. Wolpert (Dist Teacher Scholar), G. Yang, J. Yorke (Dist Univ Prof, Chair)
Associate Professors: S. Cerrai, W. Czaja, L. Koralov, D. Margetis, A. Mellet, K. Okoudjou, N. Ramachandran, P. Smith (Assoc Dean), T. VonPetersdorff, C. Warner, H. Winkelnkemper
Assistant Professors: M. Cameron, A. Gholampour, K. Melnick, C. Zickert
Lecturers: C. Cremins (Senior Lecturer), J. Daberkow (Senior Lecturer), D. Franklin (Senior Lecturer), F. Gulick (Senior Lecturer), M. Jarchow, K. McLaren (Senior Lecturer), S. Orsetti, T. Pilachowski, W. Schildknecht (Acad Prog Coord), E. Shearn, J. Stone (Senior Lecturer), C. Terpos, K. Truman (Acad Advisor), J. Wyss-Gallifent (Senior Lecturer)
Affiliate Professors: D. O'Leary, G. Stewart (Dist Univ Prof)
Adjunct Professors: M. Bhatia, J. Xu
Professors Emeriti: W. Adams, J. Alexander, J. Auslander, I. Babuska (Dist Univ Prof Emeritus), C. Berenstein, K. Berg (Assoc Prof Emeritus), M. Brin, J. Cooper, E. Correl, D.Lay (Dist Teacher Scholar), J. Dancis (Assoc Prof Emeritus), G. Ehrlich, R. Ellis, J. Fey, J. Goldhaber, R. Good, P. Green, M. Heins, G. Helzer (Assoc Prof Emeritus), R. Herb, J. Horvath, R. Johnson, R. Kellogg, H. King, A. Kleppner, G. Lehner, R. Lipsman, N. Markley, U. Neri, F. Olver, J. Osborn, J. Owings, J. Sather (Assoc Prof Emeritus), D. Schneider (Assoc Prof Emeritus)
Visiting Faculty: M. Macasieb (Visit Asst Prof)

The Major

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.

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.

Academic Programs and Departmental Facilities

Combined B.S./M.A. Program in Mathematics

The Department of Mathematics offers a combined B.S./M.A. degree program for students with exceptional ability and interest in mathematics. Students enrolled in the Combined Degree Program may count up to 9 credits of coursework taken for their undergraduate degree toward the M.A. degree as well. For further information, please consult the Mathematics Department Web Page: www.math.umd.edu/undergraduate/majors/bsma.html.

Placement in Courses

The Department of Mathematics has a large offering to accommodate a great variety of backgrounds, 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-Examination. Students are urged to consult with advisors from the Department of Mathematics to assist with proper placements.

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.

Requirements for the Major

There are three tracks for the major: the traditional 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.

 

TRADITIONAL TRACK  
    Credits
  Introductory Sequence *  
MATH140 Calculus I 4
MATH141 Calculus II 4
MATH240 Introduction to Linear Algebra 4
MATH241 Calculus III 4
  One from:  
MATH246 Differential Equations for Scientists and Engineers 3
MATH341 Multivariable Calculus, Linear Algebra, Differential Equations 4
MATH414 Differential Equations  3
MATH436 Differential Geometry of Curves and Surfaces I 3
MATH462 Partial Differential Equations for Scientists and Engineers 3
  Eight MATH/AMSC/STAT courses** at the 400-level or higher; must include:
MATH410 Advanced Calculus I***  3
   One From:  
MATH401 Applications of Linear Algebra 3
MATH403 Introduction to Abstract Algebra 3
MATH405 Linear Algebra 3
   One From:  
AMSC460 Computational Methods 3
AMSC466 Introduction to Numerical Analysis I 3
  Depth Requirement; a one year sequence chosen from the following:  
MATH 410/411 Advanced Calculus I and II 6
MATH 410/412 Advanced Calculus I / Adv Calc w/Applications 6
MATH 403/404 Introduction to Abstract Algebra / Field Theory 6
MATH 403/405 Introduction to Abstract Algebra / Linear Algebra 6
STAT 410/420 Introduction to Probability Theory / Introduction to Statistics 6
     
  Electives+  
  400 level courses (may not include: MATH 400, 461, 478, 480-484, STAT 464)
 
One from:
 
  (A student may be exempt from this requirement if (s)he can demonstrate adequate programming knowledge from prior course or work experience.)  
CMSC106 Introduction to C Programming 4
CMSC114 Computer Science I 4
CMSC122 Introduction to Computer Programming via the Web 3
CMSC131 Object-Oriented Programming I 4
CMSC132 Object-Oriented Programming II 4
ENAE202 Aerospace Computing 3
ENEE114 Programming Concepts for Engineering 4
PHYS165 Introduction to Programming in the Physical Sciences 3
  Supporting three-course sequence  
  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.) Choose one sequence:  
  Sequence One  
PHYS161 General Physics: Mechanics and Particle Dynamics 3
PHYS260/261 General Physics: Vibration, Waves, Heat, Electricity and Magnetism/Lab 4
PHYS270/271 General Physics: Electrodynamics, Light, Relativity and Modern/Lab 4
  Sequence Two  
PHYS171 Introductory Physics: Mechanics and Relativity 3
PHYS272 Introductory Physics: Fields 3
PHYS273 Introductory Physics: Waves 3
  Sequence Three  
ENES102 Statics 3
PHYS161 General Physics: Mechanics and Particle Dynamics 3
ENES220 Mechanics of Materials 3
  Sequence Four  
CMSC132 Object-Oriented Programming II 4
CMSC212 Introduction to Low-Level Programming Concepts 4
CMSC250 Discrete Structures 4
  Sequence Five  
CHEM146/147 Principles of General Chemistry/Lab 4
CHEM237 Principles of Organic Chemistry I 4
CHEM247 Principles of Organic Chemistry II 4
  Sequence Six  
CHEM131/132 Chemistry I - Fundamentals of General Chemistry/Lab 4
CHEM231/232 Organic Chemistry I/Lab 4
CHEM241/242 Organic Chemistry II/Lab 4
  Sequence Seven  
ECON200 Principles of Micro-Economics 4
ECON201 Principles of Macro-Economics 4
ECON305 Intermediate Macroeconomic Theory and Policy, OR 3
  ECON306 Intermediate Microeconomic Theory 3
  Sequence Eight  
BMGT 220 Principles of Accounting I 3
BMGT221 Principles of Accounting II 3
BMGT340 Business Finance 3
     
  * Or honors sequence: MATH 340-341.Completion of MATH 340 satisfies the requirement for MATH 241; completion of MATH 340-341 satisfies the requirement for MATH 240-241-246. 
  ** At least four courses must be taken at College Park.  
  *** Most students are strongly encouraged to complete MATH 310 prior to attempting MATH 410.
   + 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.

Secondary Education Track T
    Credits
  Introductory Sequence*  
MATH140 Calculus I 4
MATH141 Calculus II 4
MATH240 Introduction to Linear Algebra 4
MATH241 Calculus III 4
  One from:  
MATH246 Differential Equations for Scientists and Engineers 3
MATH341 Multivariable Calculus, Linear Algebra, Differential Equations 4
MATH401 Applications of Linear Algebra 3
MATH452 Introduction to Dynamics and Chaos 3
MATH462 Partial Differential Equations for Scientists and Engineers 3
AMSC460 Computational Methods 3
AMSC466 Introduction to Numerical Analysis I 3
 
Seven MATH/AMSC/STAT courses** at the 400-level or higher; must include:
 
MATH410 Advanced Calculus I*** 3
MATH430 Euclidean and Non-Euclidean Geometries  3
   One from:  
MATH402 Algebraic Structures 3
MATH403 Introduction to Abstract Algebra 3
  One from: 3
STAT400 Applied Probability and Statistics I 3
STAT410 Introduction to Probability Theory 3
   One from:  
MATH406 Introduction to Number Theory 3
MATH445 Elementary Mathematical Logic 3
MATH446 Axiomatic Set Theory 3
MATH450 Logic for Computer Science 3
MATH456 Cryptology 3
MATH475 Combinatorics and Graph Theory 3
  Electives  
  400-level MATH/AMSC/STAT course (may not include: MATH 400, 461, 478, 480-484, or STAT 464)
  One from:  
  (A student may be exempt from this requirement if (s)he can demonstrate adequate programming knowledge from prior course or work experience.)  
CMSC106 Introduction to C Programming 4
CMSC114 Computer Science I 4
CMSC122 Introduction to Computer Programming via the Web 3
CMSC131 Object-Oriented Programming I 4
CMSC132 Object-Oriented Programming II 4
ENAE202 Aerospace Computing 3
ENEE114 Programming Concepts for Engineering 4
PHYS165 Introduction to Programming in the Physical Sciences 3
  Education Requirements+  
EDCI450 Student Teaching Seminar in Secondary Education: Mathematics 1
EDCI451 Student Teaching in Secondary Schools: Mathematics 12
  Supporting Sequence  
  One of the following supporting two course sequences. These are intended to broaden the student's mathematical experience.   
  Sequence One  
CHEM131/132 Chemistry I - Fundamentals of General Chemistry/Lab 4
CHEM231/232 Organic Chemistry I/Lab 4
  Sequence Two  
PHYS161 General Physics: Mechanics and Particle Dynamics 3
PHYS260/261 General Physics: Vibration, Waves, Heat, Electricity and Magnetism/Lab 4
  Sequence Three  
BSCI105  Principles of Biology I 4
BSCI106 Principles of Biology II 4
  Sequence Four  
ASTR120  Introductory Astrophysics - Solar System 3
ASTR121 Introductory Astrophysics II - Stars and Beyond 4
  Sequence Five  
GEOL100/110  Physical Geology/Lab 4
GEOL322 Mineralogy, or 4
GEOL340 Geomorphology, or 4
GEOL341 Structural Geology, or 4
GEOL375 Introduction to the Blue Ocean 3
   Sequence Six  
AOSC200/201 Weather and Climate/Lab and 4
AOSCxxx  Any 400 level AOSC course 3
     
  * Or honors sequence: MATH 340-341.Completion of MATH 340 satisfies the requirement for MATH 241; completion of MATH 340-341 satisfies the requirement for MATH 240-241-246. 
  ** At least four courses must be taken at College Park.  
  *** Most students are strongly encouraged to complete MATH 310 prior to attempting MATH 410.
   + The student-teaching pair EDCI 450-451 is 13 credits and has 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.

Statistics Track  
    Credits
  Introductory Sequence*  
MATH140 Calculus I 4
MATH141 Calculus II 4
MATH240 Introduction to Linear Algebra 4
MATH241 Calculus III 4
  One from:  
MATH246 Differential Equations for Scientists and Engineers 3
MATH341 Multivariable Calculus, Linear Algebra, Differential Equations 4
MATH414 Differential Equations  3
  Eight MATH/AMSC/STAT courses**; must include:  
MATH410 Advanced Calculus I*** 3
STAT410 Introduction to Probability Theory  3
STAT430 Introduction to Statistical Computing and SAS  3
  One from:  
AMSC460 Computational Methods 3
AMSC466 Introduction to Numerical Analysis I 3
  One from:  
MATH401 Applications of Linear Algebra 3
MATH405 Linear Algebra 3
  One from: 3
STAT401 Applied Probability and Statistics II 3
STAT420 Introduction to Statistics 3
  Two additional courses from the following list:  
STAT4-- Any 400-level or higher STAT courses (except STAT 464)  
MATH411 Advanced Calculus II 3
MATH412 Advanced Calculus with Applications 3
MATH414 Differential Equations 3
MATH424 Introduction to the Mathematics of Finance 3
MATH464 Transform Methods for Scientists and Engineers 3
AMSC 477 Optimization 3
BIOM 402  Statistics for Human and Veterinary Medicine 3
  One from:  
  (A student may be exempt from this requirement if (s)he can demonstrate adequate programming knowledge from prior course or work experience.)  
CMSC106 Introduction to C Programming 4
CMSC114 Computer Science I 4
CMSC122 Introduction to Computer Programming via the Web 3
CMSC131 Object-Oriented Programming I 4
CMSC132 Object-Oriented Programming II 4
ENAE202 Aerospace Computing 3
ENEE114 Programming Concepts for Engineering 4
PHYS165 Introduction to Programming in the Physical Sciences 3
  Supporting three-course sequence  
  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.) Choose one sequence.  
  Sequence One  
PHYS161 General Physics: Mechanics and Particle Dynamics 3
PHYS260/261 General Physics: Vibration, Waves, Heat, Electricity and Magnetism/Lab 4
PHYS270/271 General Physics: Electrodynamics, Light, Relativity and Modern/Lab 4
  Sequence Two  
PHYS171 Introductory Physics: Mechanics and Relativity 3
PHYS272 Introductory Physics: Fields 3
PHYS273 Introductory Physics: Waves 3
  Sequence Three  
ENES102 Statics 3
PHYS161 General Physics: Mechanics and Particle Dynamics 3
ENES220 Mechanics of Materials 3
  Sequence Four  
CMSC132 Object-Oriented Programming II 4
CMSC212 Introduction to Low-Level Programming Concepts 4
CMSC250 Discrete Structures 4
  Sequence Five  
CHEM146/147 Principles of General Chemistry/Lab 4
CHEM237 Principles of Organic Chemistry I 4
CHEM247 Principles of Organic Chemistry II 4
  Sequence Six  
CHEM131/132  

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: MATH 402, 403, 404, 405, 406, 410, 411, 414, 430, 432, 436, 437, 445, 446, 452, 456, and STAT 410, 420. Students preparing for graduate school in mathematics should include MATH 403, 405, 410, 411 (or 412) and 463 (or 660) in their programs.  MATH 432 (or 730) is also desirable. 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: MATH 401,  406,   445,  470 and 475.

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 STAT 400-401. To work primarily as a statistician, one should combine STAT 400-401 with STAT 430 and at least one more statistics course, most suitably, STAT 440.   A deeper sequence is STAT 410, 420, 430. 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, MATH 424, STAT 400, 401, 430, 440 should be considered.  To prepare for graduate work, STAT 410 and 420 give the best background, with STAT  430, 440 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 AMSC 460, 466, MATH 431, 456, 475 and STAT 430. 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 MATH 401, 412, 414, 416, 420, 452, 462, and 464.   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.

Requirements for the Minor

The Department of Mathematics offers Minors in the following areas:    

Actuarial Mathematics    
Mathematics
Statistics

A Minor offers a structured program of study outside a student's major. See www.math.umd.edu/undergraduate/opportunities for detailed information.

Advising

Advising for math majors is mandatory. Students are required to sign up for an advising appointment online, beginning the week before early registration. Students who have been away more than two years may find that due to curriculum changes the courses they have taken may no longer be adequate preparation for the courses required to complete the major. Students in this situation must meet with the Department Advisor to make appropriate plans.

Undergraduate Research Experiences

There are a variety of undergraduate research opportunities in mathematics at Maryland.  For detailed information see
www.math.umd.edu/undergraduate/opportunities/reu.html

Honors Program

The Mathematics Honors Program is designed for students showing exceptional ability and interest in mathematics. Its aim is to give a student the best possible mathematics education. Participants are selected by the Departmental Honors Committee during the first semester of their junior year. A precise statement of the requirements may be found at www.math.umd.edu/undergraduate/opportunities/DepartmentalHonors.html

The department also offers a special department honors sequence MATH 340-341 for promising freshmen with a strong mathematical background (including calculus). Enrollment in the sequence is by invitation. Participants in Honors College may also enroll in special honors sections of the lower-level mathematics courses (MATH 140H, 141H, 240H, 241H, 246H). Students in Math 340-341 and the special honors sections need not be math majors.

The mathematics departmental honors sequence and the Honors College program are distinct, and enrollment in one does not imply acceptance in the other.

 

Student Societies and Professional Organizations

There are several student-run groups within the department: the Math Club, Pi Mu Epsilon, and Women in Math.  For information, please visit:

www.math.umd.edu/undergraduate/mathclub/

www.math.umd.edu/undergraduate/mathclub/1.Home.html

www-users.math.umd.edu/~wim/

Awards and Recognition

Aaron Strauss Scholarships:   One is awarded each spring to an outstanding non-graduating math major. The recipient receives full remission of (in-state) tuition for the following academic year. Applications may be obtained early in the previous spring semester from the Mathematics Undergraduate Office, 1117 Mathematics Building.

Aziz Mathematics Scholarship: The Aziz scholarship is the department's highest award of mathematical excellence for a non-graduating math major.  When eligible, the receipient receives a monetary award to cover in-state tuition in the following academic year. 

Dan Sweet Scholarship:  A one-semester stipend awarded to a math major on the basis of merit.

Edgar Krahn Scholarship: A monetary award is made on the basis of performance in the Maryland High School Mathematics Competition.

Euclid Teaching Assistantship:  This is an opportunity for a math major planning to teach in secondary or middle school to work as an undergraduate TA. Apply in the spring for the following year

Higginbotham Prize: A monetary award is made to an outstanding junior math major in the spring. 

Milton Abramowitz Award: A monetary award is made to an outstanding junior or senior math major in the spring.

Outstanding Senior Award: A monetary award is made to the outstanding graduating math major.

Secondary Education-Mathematics (SEM) Scholarship: Up to two are awarded in the spring to Secondary Education-Mathematics double majors.

Strauss Teaching Assistantship:  This is an opportunity for outstanding math majors to work as an undergraduate TA. Apply in the spring for the following year.

For further information on awards, consult www.math.umd.edu/undergraduate/opportunities

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