
Undergraduate Record 20112012 [ARCHIVED RECORD]
Mathematics


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Requirements for Major
Normally, the calculus sequence MATH 1310, 1320, and 2310 or its equivalent must be completed before a student can declare a major in mathematics. At least a 2.200 average in the calculus sequence and a minimum grade of C in MATH 2310 or its equivalent are required. However, the department may grant special permission to declare a major to a student who has only completed MATH 1310 and 1320, and at least one mathematics course (other than MATH 2310 or its equivalent) which could be counted toward the major in mathematics, provided the student completes MATH 2310 or its equivalent in the semester following the declaration of a mathematics major.
To graduate with a major in mathematics the student must show computer proficiency by completing CS 1110, CS 1111, CS 1112, CS 1120, or PHYS 2660, or an approved equivalent course with a grade of C or higher. This should be done as early as possible.
To help guide the student through the major, the mathematics department offers five concentrations. Completion of one of these concentrations is required. Each concentration contains a set of nine required mathematics courses (approximately 28 credits). To graduate, a student must obtain minimum grades of C in seven of these courses and C in the other two. Up to two courses that are being counted for another College major or another College minor can also be counted for the major in mathematics.
For students at U.Va. from the start, up to two courses that are taken from outside the University and which are equivalent to College mathematics courses may be offered for the College mathematics major. For transfer students, the allowed number of transferred mathematics courses toward mathematics majors is decided casebycase by the Director of Undergraduate Programs with advice from the transfer credit advisor.
Certain substitutions are allowed in all options, for example, MATH 5310 for MATH 3310, MATH 5651 for MATH 3351, MATH 5652 for MATH 3354, and PHYS 5630 for MATH 4300. PHIL 5420 Symbolic Logic is an approved elective for both the major and minor in mathematics. A. The Basic Concentration
Students fulfilling the requirements for this option have a wide range of career opportunities, from law to business to any field that requires deductive, logical reasoning skills.
This traditional program for the mathematics major provides an overview of key areas: B. The Graduate Preparatory Concentration
This concentration is for the student who plans to attend graduate school in mathematics or an allied field. The program emphasizes the fundamental ideas of mathematics with substantial work in proving and understanding the basic theorems. It consists of:  MATH 3250  Ordinary Differential Equations Credits: 4
 MATH 3340  Complex Variables with Applications Credits: 3
 MATH 5310  Introduction to Real Analysis Credits: 3
 MATH 5651  Advanced Linear Algebra Credits: 3
 MATH 5652  Introduction to Abstract Algebra Credits: 3
 Four mathematics courses at the 3000 level or higher. Courses without a MATH prefix, and not listed below as an approved substitution or elective, are generally not allowed. At least two electives must be MATH courses
(Students may wish to take MATH 3310 in preparation for MATH 5310, MATH 3351 in preparation for MATH 5651, and MATH 3354 in preparation for MATH 5652.)
This constitutes the minimum expected of an incoming graduate student in most programs nationwide. The department strongly recommends MATH 5330 (Advanced Multivariate Calculus), as well as courses in differential geometry (MATH 5720) or topology (MATH 5770). The Department may recommend access to its 7000level graduate courses for undergraduates with particularly strong capabilities.
C. The Probability and Statistics Concentration
This concentration is designed to give the student a good theoretical underpinning in probability and statistics, as well as the opportunity to go deeper in these fields. The program can lead to a Master of Science in Statistics with one additional year of course work, if additional courses in statistics are taken in the fourth year. (Those interested in the M.S. in Statistics should contact the graduate advisor in the Department of Statistics prior to the beginning of their fourth year.) The requirements for the concentration are the following: One additional course chosen from:
 MATH 5310  Introduction to Real Analysis Credits: 3
 STAT 3130  Design and Analysis of Sample Surveys Credits: 3
 STAT 5130  Applied Multivariate Statistics Credits: 3
 STAT 5160  Experimental Design Credits: 3
 STAT 5170  Applied Time Series Credits: 3
 STAT 5190  Introduction to Mathematical Statistics Credits: 3
D. The Financial Mathematics Concentration
This program provides the student with a broad background of basic mathematics, which is essential for an understanding of the mathematical models used in the financial markets. The mathematics of modern finance includes probability, statistics, regression, time series, partial differential equations, stochastic processes, stochastic calculus, numerical methods, and analysis. The program consists of: Two additional courses chosen from:
Two courses chosen from:
(completing all four courses are recommended) E. Fiveyear Teacher Education Program
This option leads to both Bachelor of Arts and Master of Teaching degrees after five years. The program is for both elementary and secondary teachers and is administered by the Curry School of Education.
The following are the required mathematics courses for this program (the Curry School has additional requirements): Distinguished Majors Program in Mathematics
The department offers a Distinguished Majors Program (DMP) to qualified majors in mathematics. The departmental committee for the DMP grants admission to the program, usually at the end of the student’s fourth semester. Criteria for acceptance into the program are based on the GPA in mathematics, letters of recommendation from mathematics instructors, and the cumulative GPA in the College (which should be near 3.400 or higher).
The DMP is the same as the graduate school preparatory concentration, except that in the fourth year the students take the seminar course MATH 5830 in which they give an hour lecture and prepare a written exposition of their work in the seminar under faculty guidance. As with the concentrations, the DMP must consist of at least nine courses.
Three levels of distinction are possible: distinction, high distinction, or highest distinction. The departmental recommendation for the level of distinction to be awarded is based on the quality of the student’s seminar presentations, the overall work in the DMP, and the entire major program, as well as the student’s College GPA. Requirements for Minor in Mathematics
Students who wish to declare a minor in mathematics must complete the calculus sequence through MATH 2310 or its equivalent with at least a 2.000 average.
To graduate with a minor in mathematics a student must complete five courses approved by the department of mathematics with minimum grades of C in three of the courses and minimum grades of C in the other two. An approved course must carry at least three credits. Currently, the approved courses are those from the College department of mathematics with the MATH mnemonic numbered 3000 or higher. Either MATH 3310 or MATH 3354 should be one of the five approved courses. Courses with the APMA and STAT mnemonics, as well as courses from other departments or institutions can be taken if approved by the undergraduate committee.
Up to two courses that are being counted for another College major or another College minor can also be counted for the minor in mathematics.
Up to two courses that are taken from outside the University and which are equivalent to College mathematics courses may be offered for the College mathematics minor. Echols Mathematics Club
Echols Mathematics Club is an undergraduate club for mathematics students that sponsors lectures, mathematics films, problem solving sessions for the Putnam Mathematical Competition and other similar activities Elementary Courses in Mathematics
The entering College student has a variety of courses in mathematics from which to choose. Among those that may be counted toward the College area requirement in natural science and mathematics, are several options in calculus, elementary (noncalculus based) courses in probability and in statistics, and courses dealing with computer techniques in mathematics. Precommerce students are required to take a statistics course and one other mathematics course, usually MATH 1110, 1210, 1220, or 1310.
MATH 1030 (precalculus) is available for students who need to improve basic skills that are required in other courses such as calculus, chemistry, psychology, economics, and statistics. However, it may not be counted toward the area requirement in natural science and mathematics. Students planning to major in the social sciences, arts, or humanities who wish to take a mathematics course but omit the study of calculus may choose from MATH 1110 (Elementary Probability Theory) and MATH 1140 (Financial Mathematics). Even though it is not a prerequisite, MATH 1110 is frequently taken prior to Introductory Statistics. MATH 1150 and 1160 are introductory courses that investigate familiar areas of elementary mathematics at a deeper level and are intended for first and secondyear nonmajors, especially those preparing to teach in elementary and middle schools.
In MATH 1140 the students learn the mathematics needed to understand and answer a variety of questions that arise in everyday financial dealings. The emphasis in this course will be on applications, including simple and compound interest, valuation of bonds, rates of return on investments, and more. Although the topics in this course are drawn primarily from business and economics, students of all majors are welcome and should find the applications interesting and relevant. Calculus Sequence
The study of calculus is the foundation of college mathematics for students planning to major in mathematics or the physical sciences or anticipating a career or graduate study in any of the natural sciences, engineering, or applied social sciences (such as economics). There are essentially two programs of study available in calculus:
• MATH 1210, 1220 is a terminal oneyear sequence intended for business, biology, and social science majors;
• MATH 1310, 1320, 2310 is the traditional calculus sequence intended for students of mathematics and the natural sciences, as well as for students intending to pursue graduate work in the applied social sciences;
The MATH 1210, 1220 sequence is unacceptable as a prerequisite for mathematics courses numbered 2310 and above. Students anticipating the need for higher mathematics courses such as MATH 3250 (Differential Equations), MATH 3100 (Probability) or STAT 3120 (Statistics) should instead elect the MATH 1310, 1320, 2310 sequence. Credit is not allowed for both MATH 1210 and 1310 (or its equivalent). MATH 2310 is the prerequisite for many advanced mathematics courses. Advanced Placement
Students who have previously passed a calculus course in high school may elect MATH 1220, 1310, 1320, or 2310 as their first course, depending on placement, preparation, and interest. A strong high school calculus course is generally adequate preparation for MATH 1320 as a first calculus course, even if advanced placement credit has not been awarded for MATH 1310. Students planning to take any advanced course in mathematics should not take MATH 1220, because credit for that course must be forfeited if the student takes MATH 1320 (or its equivalent). Wellprepared students (who place out of both MATH 1310 and 1320) may choose either MATH 2310 or 3250 (Differential Equations) as their first course.
Advanced first year students are encouraged to consider the honors section of Multivariate Calculus MATH 2315.
Advanced placement credit in the calculus sequence is granted on the basis of the College Entrance Examination Board Advanced Placement Test (either AB or BC). A score of 4 or 5 on the AB test or on the AB subscore of the BC test gives the student credit for MATH 1310. A score of 4 or 5 on the BC test gives the student credit for both MATH 1310 and 1320. Substitutions
There are numerous instances of equivalent courses offered by the Department of Mathematics as well as by the Department of Applied Mathematics in the School of Engineering and Applied Science. A student may not offer for degree credit two equivalent courses (e.g., MATH 1310 and APMA 1090, or MATH 1210 and MATH 1310). The following are equivalent courses from the School of Engineering and Applied Sciences:
• APMA 1090 and MATH 1310  Calculus I Credits: 4
• APMA 1110 and MATH 1320  Calculus II Credits: 4
• APMA 2120 and MATH 2310  (Multivariate) Calculus III Credits: 4
• APMA 2130 and MATH 3250 Ordinary Differential Equations Credits: 4
• APMA 3102 and MATH 4040  Discrete Mathematics Credits: 3
• APMA 3080 and MATH 3351  Elementary Linear Algebra Credits: 3
• APMA 3100 and MATH 3100  Introduction to Probability Credits: 3
• APMA 5070 and MATH 4300  Elementary Numerical Analysis Credits: 3
• STAT 3120 and MATH 3120  Introduction to Statistics Credits: 3
Standard Allowed electives
CS 4102  Algorithms Credit: 3
ECON 4010  Game Theory Credit: 3
SYS 3021  Deterministic Decision Models Credit: 3 
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