Mathematics

Normally, the calculus sequence MATH 131, 132, and 231 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 231 or its equivalent are required. However, the department may grant special permission to declare a major to a student who has only completed MATH 131 and 132, and at least one mathematics course (other than MATH 231 or its equivalent) which could be counted toward the major in mathematics, provided the student completes MATH 231 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 101, CS 120 or PHY 254, 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.

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.

Certain substitutions are allowed in all options, for example, MATH 531 for MATH 331, MATH 551 for MATH 351, MATH 552 for MATH 354, and PHYS 553 for MATH 430. PHIL 542 Symbolic Logic is an approved elective for both the major and minor in mathematics.

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:

• Four electives at the 300 level or higher, of which at least two are MATH courses Credits: 12

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: 

Four electives at the 300 level or higher, of which at least two are MATH courses. (Students may wish to take MATH 331 in preparation for MATH 531, MATH 351 in preparation for MATH 551, and MATH 354 in preparation for MATH 552.)

This constitutes the minimum expected of an incoming graduate student in most programs nationwide. The department strongly recommends MATH 533 (Advanced Multivariate Calculus), as well as courses in differential geometry (MATH 572) or topology (MATH 577). The Department may recommend access to its 700-level graduate courses for undergraduates with particularly strong capabilities.

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:

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:

Completing all four courses is recommended.

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. Required courses include:

The Curry School has additional requirements for this program.

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 583 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.

Students who wish to declare a minor in mathematics must complete the calculus sequence through MATH 231 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 300 or higher. Either MATH 331 or MATH 354 should be one of the five approved courses. Courses with the STAT mnemonic or 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.

For more information, contact Thomas Kriete, Undergraduate Program Chair, tlk8g@virginia.edu, 924-4932, Room 205, Kerchof Hall, or Zoran Grujic, Mathematics Major Advisor, zg7c@virginia.edu, Room 329, Kerchof Hall, or see the Departmental Homepage, http://www.math.virginia.edu.

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 (non-calculus based) courses in probability and in statistics, and courses dealing with computer techniques in mathematics. Pre-commerce students are required to take a statistics course and one other mathematics course, usually MATH 111, 121, 122, or 131.

MATH 103 (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 111 (Elementary Probability Theory) and MATH 114 (Financial Mathematics). Even though it is not a prerequisite, MATH 111 is frequently taken prior to Introductory Statistics. MATH 115 and 116 are introductory courses that investigate familiar areas of elementary mathematics at a deeper level and are intended for first- and second-year non-majors, especially those preparing to teach in elementary and middle schools.

In MATH 114 the students study 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.

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:

1. MATH 121, 122 is a terminal one-year sequence intended for business, biology, and social science majors;
2. MATH 131, 132, 231 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 121, 122 sequence is unacceptable as a prerequisite for mathematics courses numbered 231 and above. Students anticipating the need for higher mathematics courses such as MATH 325 (Differential Equations) or MATH 310, 312 (Probability and Statistics) should instead elect the MATH 131, 132, 231 sequence. Credit is not allowed for both MATH 121 and 131 (or its equivalent). MATH 231 is the prerequisite for many advanced mathematics courses.

Students who have previously passed a calculus course in high school may elect MATH 122, 131, 132, or 231 as their first course, depending on placement, preparation, and interest. A strong high school calculus course is generally adequate preparation for MATH 132 as a first calculus course, even if advanced placement credit has not been awarded for MATH 131. Students planning to take any advanced course in mathematics should not take MATH 122, because credit for that course must be forfeited if the student takes MATH 132 (or its equivalent). Well-prepared students (who place out of both MATH 131 and 132) may choose either MATH 231 or 325 (Differential Equations) as their first course.

Exceptionally well-prepared students (who place out of both MATH 131 and 132) may choose either MATH 231 or 325 (Differential Equations) as their first course.  Advanced first year students are encouraged to consider the honors section of Multivariate Calculus MATH 231H.

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 131. A score of 4 or 5 on the BC test gives the student credit for both MATH 131 and 132. 

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 131 and APMA 109, or MATH 121 and MATH 131). Up to two courses, taken from outside of the University and which are equivalent to College mathematics courses, may be offered for the College mathematics major or minor. The following are equivalent courses from the School of Engineering and Applied Sciences:

APMA 109 and MATH 131 Calculus I Credits: 4

APMA 111 and MATH 132 Calculus II Credits: 4

APMA 212 and MATH 231 (Multivariate) Calculus III Credits: 4