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Handbook for Mathematics Majors

General Information for All Mathematics Options, and a Description of the Traditional Option

Introduction
The purpose of this handbook is to advise you, the mathematics student, about the Mathematics Department and the curriculum for the Bachelor of Science degree in Mathematics. There are four different paths or options that you may follow towards a BS degree in Mathematics:

(1) The Traditional Option
(2) The Applied and Computational Mathematics Option (ACM)
(3) The Applied Discrete Mathematics Option (ADM), and
(4) The Educational Option.

The Traditional Option, as its name implies, yields a broad and flexible background in mathematics. The other three options are more specialized. The ACM is designed for students who are confident that they want to have an applied mathematics career in an area closely associated with physics or some form of engineering. The ADM is designed for students who are confident that they want to have an applied mathematics career in an area closely associated with computer science, statistics, or actuarial science. The Education Option is designed for students who are confident that they want to teach high- or middle-school mathematics.

Often students will begin their studies in the Traditional Option, and later change to one of the other three options when they become more sure of the path that they wish to pursue. One, however, can acquire many aspects of the three specialized options within the Traditional Option, because it also requires some degree of specialization in an applications area and provides career development features. The three specialized options are each less general, but bring particular career paths into sharper focus. Each of the four options provides an excellent foundation for graduate study, either in mathematics or in an applications area.

This handbook will give details about requirements that are common to all four options (such as the University Core Curriculum), and it will also describe the graduation checksheet for the Traditional Option. Three other brochures are available from the Mathematics Department that describe the other three options more carefully and include their graduation checksheets.

Department Location
The Mathematics faculty offices are located on the 4th and 5th floors of McBryde. The departmental office is 460 McBryde. The receptionist on duty can answer many questions you may have and direct you to an appropriate person for answers to other questions. Course outlines, lists of reference texts for specific courses, and other general information brochures are also available.

The Scholarship Program

The department has several scholarship programs. The main ones are the Hatcher Scholarship, the Morris Scholarship, the John C. and Elsie M. Layman Scholarship, the Caldwell Scholarhip, the Dean's Scholarship and the Roselle Scholarship.

The Hatcher Scholarship Fund was established in 1975 by the late T. W. Hatcher, head of the Mathematics Department from 1941 to 1966. Income from the endowment is placed in an operating account to be used for scholastic merit scholarships for undergraduates majoring in mathematics. As a general rule, 15- 20 scholarships for up to $1,000 per year are awarded; distributed among incoming freshmen and continuing students.

The A. V. Morris Scholarship was established in 1989 by Laura Burrows, Mr. Morris's daughter. Professor Morris worked in the department from 1923 to 1965. Three to four students are supported each year for up to $1,000. These are merit-based scholarships.

The Roselle Scholarship is awarded to a rising senior in mathematics and is chosen on a merit basis. Dr. Roselle came to Virginia Tech as a faculty member in 1974, became Dean of the Graduate School in 1979, and served as the University Provost from 1983-1987. The award is for $500.

The Layman Scholarship is given in honor of John C. and Elsie Layman by their son, John W. Layman. Both John Laymans were long-standing members of the Mathematics faculty. The awards are for one $1,000 or two $500 scholarships and are intended for incoming freshmen from public schools in rural neighboring areas.

The Caldwell Scholarship is being endowed by Patricia Ann Caldwell, a prominent mathematics alum and is intended for out-of-state women and is based on achievement, character, and appreciation of mathematics.

The Dean's Scholarship of $1,000 is given to an entering freshmen and is funded by the Dean of the College of Arts and Sciences. As the other four scholarships described, it is a merit-based award.

For further scholarship information, contact Dr. Charles Parry or the chairman of the Mathematics Scholarship Committee.

Governance of the Undergraduate Curriculum
The Undergraduate Mathematics Curriculum is ultimately governed by the Mathematics Faculty and the Department Head. However, the faculty and head are advised by the Undergraduate Program Advisory Committee (UPC) and advisory committees for each of the three specialized options. These committees are concerned with all matters pertaining to the curriculum of the undergraduate mathematics majors. The committees discuss all suggested changes in requirements, all suggested changes in 3000- and 4000-level mathematics courses in the curriculum, and all suggested new texts. Finally, the committees rule on requests of individual majors to depart from the standard programs.

Student Advisors
You are assigned a faculty advisor to help you in planning your undergraduate program and to help you in registering for classes. An attempt is made to keep you with the same advisor for your entire undergraduate career. Your advisor and Sandy Blevins will keep records of your progress toward a degree and keep you posted on these matters. You will also be aided by your advisor in settling difficulties that may arise with the Registrar's Office at the time of your graduation.

In addition to your specific advisor, the Mathematics Department has two designated Career Advisors, Dr. Lizette Zietsman. Her task is to work with your academic advisor in providing you with information which will aid you in planning a career-oriented program. Materials concerning careers and campus interviews are regularly posted on the bulletin board on the northwest wall of fourth floor, McBryde Hall. In connection with this endeavor, the Mathematics Department has designed a brochure, "Mathematical Careers." Copies may be obtained in McBryde 460.

We strongly urge you to inform the Mathematics Department of your e-mail address. (Send it to Blevins @ math.vt.edu.) In this way we can keep you much better informed; especially of activities and career opportunities. You can obtain e-mail connection instructions from Sandy Blevins in 460 McBryde.

The Undergraduate Mathematics Curriculum
The curriculum of each of the four options is designed to give you a solid foundation in the basic areas of mathematics with supporting background in allied areas. The specific requirements are:

University:
(1) All students are required to have a 2.000 QCA for all courses attempted, and for all courses in the student's major. The in-major QCA is not printed on the grade report, but is available on request in McBryde 460 and on your DARS report.

(2) No course used to fulfill major, minor, or University/College core curriculum requirements may be taken pass/fail.

(3) Only students with QCA's of 2.5 or above and who have completed at least 30 credit hours at Virginia Tech may take elective courses pass/fail (unless the course is offered only P/F). Students may take no more than 10% of the hours taken at Virginia Tech on a P/F basis. The 10% limit includes courses offered P/F only.

(4) Of the 120 hours required for graduation, a student may count no more than 2 hours of Physical Education activity credit, 8 hours of Music Ensemble (MUS 3114 and 3414), and 8 hours of Independent Study and/or Undergraduate Research (2974, 2994, 4974, 4994). There is a University foreign language requirement, but it is covered by the more stringent Arts & Sciences requirement (see below).

(5) Students entering prior to Fall 2005 must satisfy a six-credit writing intensive requirement in their major; writing intensive courses in Mathematics are Math 3034 and 4044. For students entering Fall 2005 or later, The ViEWS (Visual Expression, Written and Spoken Communication) requirement is met by required courses for the major.

College:
The College of Science requires 120 total hours for graduation. Area 4 now requires a single eight-hour laboratory sequence in Biology, Chemistry, Geology, or Physics. Mathematics majors must take Math 1205- 1206 or its equivalent to satisfy the Area 5 core requirement.

(1) A maximum of 60 hours in mathematics courses.

(2) FOREIGN LANGUAGES: Successful completion of one of the following: a) The third year (level III) of one foreign language in secondary school. b) The 1106 course in Chinese, French, German, Greek, Italian, Japanese, Latin, Portuguese, Russian, or Spanish, including any prerequisites.

(i) With two years of high school credit, 1105 can be taken P/F, but 1106 must be A/F. Both 1105 and 1106 may be used as hours of credit towards graduation.

(ii) With less than two years of high school credit, both 1105 and 1106 must be taken A/F, but neither can be used as hours of credit towards graduation.

c) A score of 500 or more on the CEEB Achievement Test.

d) An examination in a language not taught at Virginia Tech with consent of the Department of Foreign Languages; arrangements made through the department (does not carry credit towards graduation).

(3) WRITING AND DISCOURSE (Area 1 - Freshman English): Successful completion of one of the following:

a) ENGL 1105, 1106; or ENGL H1204.

b) ENGL 1106, if student received Advanced Standing (with credit) for ENGL 1105.

c) Advanced-Placement Score of 4 or 5.

(4) HUMAN IDEAS, CULTURAL TRADITION, AND VALUES (Area 2 - Mostly Humanities):

Any six hours of the following courses: AAEC 2244 (AHRM 2244), 2424; AHRM 2244 (AAEC 2244); *ARCH 3115, *3116; *ART 2385*, 2386*, 3084*, 3184*, 3284*, 3384*, 3484*, 3584*, 3784*, 3884*; AFST 1714; CLA 2444 (ENGL 2444 and HUM 2444), 2454 (ENGL 2454 and HUM 2454); COMM 2064; EDPE 3114; ENGL 1604, 1614, 1624, 1634, 1644, 1654, 1664, 1674, 2324, 2334, 2444 (CLA 2444 and HUM 2444), 2454 (CLA 2454 and HUM 2454), 2515, 2516, 2525, 2526, 3404 (FR 3404), 3414 (GER 3414), 3424 (RUS 3424), 3434 (SPAN 3434), 3534, 3644, 4165, 4166; FR 3205, 3206, 3305, 3306; GER 3305, 3306, SPAN 3204, 3214, 3314, 3324, FR 3404 (ENGL 3404), GER 3414 (ENGL 3414), RUS 3424 (ENGL 3424), SPAN 3434 (ENGL 3434), FR 2714 (HUM 2714), GER 2724 (HUM 2724) RUS 2734 (HUM 2734), SPAN 2744 (HUM 2744), SPAN 2754 (HUM 2754); FOR 2554; HIST 1024, 1025, 1026, 2054 (STS 2054); STS 1504, 2054 (HIST 2054), 2354, 3105, 4304, HORT 3524; HUM 1114, 1124, 1214, 1224, 1314, 1324, 1604, 1704, 1914, 1924, 2204, 2444 (ENGL 2444 and CLA 2444), 2454 (ENGL 2454 and CLA 2454), 2714 (FR 2714), 2724 (GER 2724), 2734 (RUS 2734), 2744 (SPAN 2744), 2754 (SPAN 2754), 4404; JUD 2414 (REL 2414); LAR 4034; LDRS 1015; MUS 1005, 1006, 1104*, 2115*, 2116*, 3115*, 3116*; PHIL 1204, 1304, 2115, 2116, 2125, 2126, 2304, 2605, 2606, 3015 (PSCI 3015), 3016 (PSCI 3016), 3314, 3454, 4204, 4214, 4224, 4304, 4334, 4614; PSCI 3015 (PHIL 3015), 3016 (PHIL 3016); REL 1014, 1024, 1034, 1044, 2124, 2234 (WS 2234), 2424, 3024, 3214, 3224, 3414, 3424; SOC 2024 (Only with AFST 1714); *TA 2014*, 2024*; UAP 4264; WS 1824, 2224, 2244, 2254.

*Courses marked with an asterisk are also listed in AREA 6; They CANNOT count in both areas.

(5) SOCIETY AND HUMAN BEHAVIOR (Area 3 - Mostly Social Sciences):

Any six hours of the following courses: AAEC 1005, 1006, 1014 (HIST 1014); AS 3215; COMM 1014; ECON 2005, 2006, H2025, H2026; HD 1004, 3004; GEOG 1004, 1014, 2055; HIST 1004, 1014, 1115, 1116, H2104, 3155, 3156, 3505, 3506, 3705 (STS 3705), 3706 (STS 3706); STS 3705 (HIST 3705), 3706 (HIST 3706), 4704 (WS 4704); IS 2055 (PSCI 2055), IS 2056 (PSCI 2056); LDRS 1016; MN 4005; PSCI 1014, 1024, 2055 (IS 2055), 2056 (IS 2056); PSYC 2004, 2034, 2044, 2054, 2064, 2084, 3014; SOC 1004, 1014, 2004, 2014, 2024, 2304, 2504, 3004, 3304, 3504, 3604, 4304; SPIA 1004; UAP 1024, 2014, 2024, 3014; WS 2264, 4704 (STS 4704).

(6) SCIENTIFIC REASONING AND DISCOVERY (Area 4 - Natural Sciences): Any of the eight-hour sets listed below

BIOL 1005, 1006 General Biology 1015, 1016 General Biology Laboratory
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BIOL 1105, 1106 Principles of Biology 1115, 1116 Principles of Biology Laboratory
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BIOL 1205, 1206 Honors Biology (Includes Lab)

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CHEM 1015, 1016 Introduction to Chemistry 1025, 1026 Introduction to Chemistry Laboratory
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CHEM 1035, 1036 General Chemistry 1045, 1046 General Chemistry Lab

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CHEM 1074, 1084 General Chemistry for Engineers and General Chemistry Lab for Engineers

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CHEM H1074, H1084 Honors General Chemistry for Engineers and Honors General Chemistry Lab for Engineers

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GEOL 1004, 1104 Physical Geology and Physical Geology Laboratory Plus either 1014, 1114 Historical Geology and Historical Geology Laboratory or 1024, 1124 Resources Geology and Resources Geology Laboratory
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PHYS 1055, 1056 Intro to Astronomy 1155, 1156 Astronomy Lab

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PHYS 2205, 2206 General Physics (Not recommended for Mathematics students) 2215, 2216 General Physics Laboratory
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PHYS 2305, 2306 Foundations of Physics (Lab is part of course - 4 credits each for 2305-2306)

(7) QUANTITATIVE AND SYMBOLIC REASONING (Area 5): Mathematics majors satisfy this requirement by taking Math 1205- 1206.

(8) CREATIVITY AND AESTHETIC EXPERIENCE (Area 6 - Visual and Performing Arts): Any one of the following courses:

AHRM 2254; ALS 1004; ARCH 1015, *ARCH 3115*, 3116*; ART 1114, *ART 2385*, 2386*, 3084*, 3184*, 3284*, 3384*, 3484*, 3584*, 3784*, 3884*; COMM 2054; EDPE 2204; ENGL 1604*, 1614*, 1634*, 2744; HORT 2164; *MUS 1104*, 2115*, 2116*, 3115*, 3116*, *TA 2014*, 2024*

*Courses marked with an asterisk are also listed in AREA 2; they cannot count in both areas.

(9) CRITICAL ISSUES IN A GLOBAL CONTEXT (Area 7): This three-hour requirement applies only to students who were freshmen in Fall, 1994, or later. Some of the listed courses are also listed in a different core curriculum area. Any such course may be used in both areas; i.e., the course "double counts."

AAEC 2464 (STS 2464, REL 2464), 3204, 3314; AS 4215; AHRM 4604; AFST 1814; BSE 4394; BIOL 2204; CEE 3104, 4554; COMM 3204 (HUM 3204); CSES 3444; ECON 4124, 4135, 4136; ENGR 1814, 2864; ENGL 1614, 3534, 3644; ENT 2004; ENSC 3604; FIN 4144; FW 2114; FOR 3784 (Wood 3784); GEOG 1014, 2034, 2055 (IS 2055, PSCI 2055), 2134, 3104, 4074, 4204, 4764 (SOC 4764, UAP 4764); GEOS 1024; HD 3314; HIST 1214, 1224, 2054 (STS 2054), 3184, 3394, 3654; STS 2054 (HIST 2054), 2464 (AAEC 2464, REL 2464); HTM 2454; HUM 3204 (COMM 3204), 2734 (RUS 2734); ISE 4304; IS 2055 (PSCI 2055), 2056 (PSCI 2056); MGT 4314; MKTG 4704; MINE 3074; MN 2104; PSCI 1024, 2055 (GEOG 2055, IS 2055), 2056 (IS 2056); PHIL 2304; PHYS 2074; PPWS 2104; REL 1024, 2234 (WS 2234), 2464 (AAEC 2464, STS 2464); RUS 2734 (HUM 2734); SOC 3504, 4764 (GEOG 4764, UAP 4764); SPIA 1004; UAP 3344, 3894, 4214, 4764 (GEOG 4764, SOC 4764); WOOD 2114, 3784 (FOR 3784); WS 3214.

Department (Traditional Option):
(See the mathematics course requirements for the other three options in their respective brochures.) The university and college requirements are supplemented by the following departmental requirements:

(1) A minimum of 43 hours of mathematics, including 1114, 1205- 1206, 1224, 2214, 2224, 3034, 3124, 3214, 3224, 3144, and 12 hours of 4000-level mathematics subject to the restrictions on the Guide Sheet at the end of this booklet. (In order to enroll in 3034, a mathematics student must either (a) obtain a C or better in the final attempt of each of 1114, 1205-1206, 1224, and either 2214 or 2224; or (b) have at least a 2.2 QCA in these courses with at most one grade of C- and no D's in the last attempt in each.)


(2) A minimum of 16 hours from a list of Mathematics- related courses given further down. The 16 hours must include either 8 hours from one discipline or 6 hours from each of two disciplines and must include one of CS 1014, 1034, 1044, 1104, 1704, or 1705.

Comments on the Traditional Curriculum

A. Math Requirements:

Math 1114, 1205-1206, and 1224 are the standard mathematics courses for your freshman year. These courses introduce you to the language, techniques and applications of elementary calculus. Credit is available for Math 1205 and 1206 through the C.E.E.B. calculus advanced-placement test. Incoming freshmen should check with the summer orientation advisor about AP credit and about credit-by-examination.

Paralleling the standard versions of Math 1114, 1206, 2214, and 2224 are "honors" sections of the same material. Honors sections cover the material in more depth than standard courses and include a few extra topics. However, there is no material presented in regular sections that is not also covered in honors sections. Admission to honors sections is by invitation only. If you are interested in honors classes and you did not receive an invitation based upon your high school record, you should consult with the chairman of the honors program, the assistant chair in mathematics, or your advisor.

In addition to Math 2214 and 2224, Math 3034 should be taken during the sophomore year. (Note the "C or better" prerequisite for 3034 given above.) Much of Math 3034 is an introduction to creating logical proofs. This course bridges a gap between the largely manipulative nature of the calculus sequence and the fundamental-reasoning nature of the junior-level courses. The difference between calculus and higher-level mathematics courses is analogous to the difference between high school algebra and high school geometry.

The junior-level courses are Math 3124 (modern algebra), Math 3214 (a course in the calculus of several variables), Math 3224 (an advanced treatment of the calculus of the freshman year), and Math 3144 (an advanced treatment of the linear algebra begun in 1114). These courses should not be viewed as applied courses, but rather as courses that build mathematical foundations necessary for most senior-level courses. Exceptional students may substitute Math 4124 for 3124, and/or Math (4225-6) for (3214 and 3224).

There are a wide variety of 4000-level courses. The student should select these courses to augment his or her chosen applications area. One may also choose fundamental extensions of junior-level courses in preparation for graduate school. Twelve hours are required. Six of these hours must come from a sequence or cluster listed on the Guide Sheet at the end of this handbook. Not more than one course is allowed from 4044, 4334, and 4344. With deparmtental permission, advanced students are also allowed to take graduate courses.

B. Math-Related Courses:
A coherent program of courses in fields other than mathematics, but in which mathematics is used significantly, is valuable as part of a general education in mathematics and is extremely valuable for employment opportunities. This is the justification for requiring you to complete 16 hours of math-related (or applications-area) courses with 8 of the hours in one area, or 6 hours in each of two areas. Students may select their own applied concentration areas. Popular concentrations recently have been in computer science, actuarial science, operations research, statistics, and physics.

One of your math-related courses must be one of the following CS courses: 1044, 1054, 1104, or 1705. (In all options except MAED, EF 1016 may be substituted for this CS requirement.) A list of other math-related courses is given on the following page. Math-related courses are (a) fundamental to a discipline that uses a significant amount of advanced mathematics, and (b) courses that use mathematical constructions or concepts that are at least as sophisticated as freshman calculus. In addition to the courses listed, you may petition the Undergraduate Program Committee for the inclusion of other courses for your program. The committee, taking into consideration your overall program, will rule on the petition on an individual basis. In particular, an Independent Study or Field Study course is sometimes allowed as a math-related course. Requests to do so are handled on an individual basis as described above.
C. Electives:
There are at least 26 hours of free electives in this curriculum. (You may obtain more electives by selecting math-related courses which also satisfy other requirements.) Exercise care in choosing your electives. You have opportunities at a university which exist nowhere else. Choosing electives is one way for you to tailor your formal education individually. The ability to choose your own applications area and free electives makes this degree both strong and flexible.

(Usually if you do not have a prerequisite for a course, you should not take the course. Sometimes, however, the listed prerequisites are not absolutely necessary or are made unnecessary by other work you have done. To corroborate the necessity of the prerequisite, you can contact a faculty member from the department of the course.)

 

List of Math Related Courses

Aerospace and Ocean Engineering: All courses

Biological Sciences: BIOL 2004, 2104, 2304, 2604, 2804, 3124, 3404, 3774, 4004, 4134, 4164 (CEE 4164, CSES 4164, ENSC 4164)

Biological Systems Engineering: BSE 3305, 3306, 3414 (CE 3414), 3504, 3514, 4144, 4424 (ME 4434), 4604

Chemical Engineering: All courses

Civil and Environmental Engineering: CEE 3104, 3304, 3314, 3404, 3414 (BSE 3414), 3424, 3514, 3604, 4104, 4144, 4164 (BIOL 4164), 4184, 4304, 4314, 4324, 4354, 4444 (AOE 4054, ESM 4444), 4504, 4534, 4544, 4594 (CSES 4594), 4674

Computer Science: All courses except CS 1004, 3604, and 4004

Crop and Soil Environmental Sciences: CSES 3634 (ENSC 3634), 4114 (ENSC 4114), 4594 (CE 4594), 4644

Economics: ECON 3104, 3204, 3224, 4424

Electrical and Computer Engineering: All courses

Engineering Science and Mechanics: All courses except ESM 1054 and 1114

Finance, Insurance and Business Law: FIN 4164

Geosciences: GEOS 3104, 4124, 4154, 4164, 4174, 4804

Industrial and Systems Engineering: ISE 2404, 3014, 3214, 3414, 3424, 3614, 4005-4006, 4015, 4016, 4204, 4234, 4404, 4414

Mechanical Engineering: All courses except ME 4005-4006, 4015, 4134, 4734, 4744, 4754

Philosophy: PHIL 3505-3506, 4514

Physics: PHYS 2305-2306, and all 3000 and up

Statistics: STAT 3005-3006, 3104, 4004, 4105-4106, 4204, 4214, 4604, 4705-4706, 4714

Special Opportunities for all Mathematics Majors

The Mathematics Honors Program

The honors program in mathematics, an extension of the honors calculus sequences, leads to the degree of Bachelor of Science in Mathematics in Honors. The requirements for participation in the Honors Program are: for freshmen, 1200 combined SAT with no less than 550 on either the verbal or mathematics sections of the exam, and top 10% of high school graduating class; for upperclassmen, the minimum requirement is a 3.4 QCA for studies completed at Virginia Tech. Several academic departments in the College of Arts and Sciences offer special Honors sections of their courses. In addition to special sections of some courses, the Honors Office sponsors a colloquia series each semester. The colloquia explore special topics not in the University Curriculum.

There are two major ways in which students can participate in Honors. The first is as a Virginia Tech Commonwealth Scholar. Scholars enjoy such privileges as priority registration and the right to take Honors courses. Secondly, it is also possible to graduate with a degree "in Honors." Students seeking the "in Honors" degree must complete six hours of Honors colloquia, six to nine hours of Honors undergraduate research or independent study, and an Honors thesis.

For more details, contact the Honors Advisior

Undergraduate Research

Mathematics majors are encouraged to sign up for Math 4494 - Undergraduate Research to obtain an experience in mathematical research. A brochure on Undergraduate Research is available from the math office or from the Chairman of the Undergraduate Research Committee. The department currently sponsors the John C. and Elsie M. Layman Prize competition for the best project and paper in Undergraduate Research. For further details, see the Mathematics WWW Homepage.

Five Year Combined Bachelor/Master's Program in Mathematics

The five-year B.S./M.S. program is intended to allow especially talented undergraduate students to progress quickly into graduate-level study. The principal feature of the program is that it allows the students to use 12 hours of graduate work simultaneously toward the completion of their bachelor's degree and a program of study leading to a master's degree. It is this ability to complete the final year of undergraduate work with the same courses that comprise the first year of graduate work that makes it possible to finish both degrees in 5 years. Undergraduates are eligible to apply for the program after they have completed 75 hours and have a QCA of at least 3.5. For more information, students should contact the Assistant Chair for Undergraduate Students.

Dual Majors
The Registrar has permission to list two majors on your undergraduate transcript if you satisfy graduation requirements for two curricula and request the Registrar to list both. Dual majors with computer science, engineering, statistics, or physics are popular choices that yield excellent degrees. You may obtain two diplomas by taking an additional 30 hours of coursework beyond the requirements of the primary major.

Minors
Any department which offers a major may offer a minor. If you desire a minor in a particular discipline, contact the appropriate department for their requirements. Minors will be listed on your undergraduate transcript.

Dual Registration in Undergraduate and Graduate Courses
During your junior or senior year you may qualify to begin work on a graduate degree while completing your bachelor's degree. You must usually have a QCA of 3.0 and be within two terms of graduation. (Any course used for one degree will not count towards the other.) For more details, see the Graduate Catalog and our Graduate Admission Committee Chair.

The Cooperative Education Program
As a math major, you are encouraged to participate in the Co-op Program. This program allows you to integrate some work experiences with your academic studies. In the program you spend your first year on campus, then alternate terms between industry and college for three years, and finally spend all of your senior year on campus. You can gain experience as well as help finance your education under the Co-op plan. For more details you are invited to visit the Co-op office in Henderson Hall or see any of the Mathematics Career Advisors.

Activities
Undergraduate and graduate students in mathematics are invited to join the Virginia Tech university chapters of MAA (The Mathematical Association of America) and SIAM (Society of Industrial and Applied Mathematics). The activities of these chapters include talks on mathematics used in government and industry, as well as social, recreational, and charitable activities.

Tech has a chapter of Pi Mu Epsilon, a national organization whose purpose is the promotion of scholarly activity in mathematics. Outstanding math majors may be nominated for membership in this organization in their junior or senior years.

The Putnam Mathematics Examination
Each December a nation-wide mathematics examination, the William Lowell Putnam Competition, is given. The examination is graded for individual performances and carries a considerable amount of prestige. In addition, each participating school selects three students whose composite score represents the school. Cash prizes are awarded to the schools whose teams rank in the top five and to the members of those teams. The individuals with the top ten scores are also awarded prizes. Finally, small cash prizes are given by the Math Department to the students who rank one, two and three among the students taking the test at Tech.

The most essential feature of the examination is that it does not test for knowledge acquired in courses. Anyone who has had calculus and ordinary differential equations is prepared to work the problems. This means that all the problems are elementary, but often quite tricky. The only way for you to prepare for the examination is to practice on previous examinations or similar problems. To this end, problem seminars are organized in the fall to work through previous examinations and to select a team for the upcoming examination. These seminars and the experience of the examination can be a rewarding mathematical experience for you. You will learn techniques which are applicable to concrete problems and will develop self-reliance in mathematics. Anyone who has a "feel" for mathematics should attend the seminars, not just math majors in the upper classes. For further information, contact Dr. Martin Klaus, 472 McBryde, klaus@math.vt.edu.

Locally Sponsored Mathematics Competitions
The faculty, alumni and friends of the Mathematics Department sponsor two contests each year, one in the fall and the other in the spring. The fall competition is open to all undergraduates at Tech and at other regional colleges and universities. It is similar in nature to the Putnam examination, although it is intended to be easier. The spring competition is open to all freshmen and sophomores at Tech. This test is based upon the material covered in the freshman/sophomore courses; Math 1114, 1205-1206, 1224, and 2214. Cash prizes are awarded to the winners of each of these contests. For further information, contact Dr. Peter Linnell.

Senior Award
In each of the four degree options, one student is selected each year as the outstanding senior. These students are given special recognition and an appropriate plaque at the commencement exercises for that class.

Preparation for Post-Graduate Endeavors
Whether you plan to seek employment immediately upon graduation or attend graduate school, you need to start investigating and planning during the latter part of your junior year. You should make use of the Career Services office, the handbook on Mathematical Careers, the Internet, and Prof. Zietsman, the Mathematics Career Advisor. (See our Web site: http://www.math.vt.edu/homelevel2/CarAdvLtr97.html. Also see the Career Services Web site: http://www.career.vt.edu/)

If you are seeking employment, you should complete a resumé during the summer between your junior and senior years. (This document should also be placed in an electronic file which can be included as part of your own World Wide Web homepage, and can be used later if you use the University’s Candidate Referral Service. Contact us for homepage instructions. You will submit a resumé for every on-campus interview for which you apply, and you will include it in your letters of inquiry. (Remember the old cliché, "You never get a second chance to make a good first impression.")

You can pick up a free Placement Manual at the Career Services office in Henderson Hall. You should treat it as your primary written source for local information. Much of the Career Services material plus much, much more is available on the Internet. You can reach a good bit of preliminary Internet material by using the Job Searching link on the Va Tech Mathematics Department homepage. You definitely want to see who is interviewing on campus, and also to see lists of companies that are hiring, but not interviewing. These two lists are posted on the Mathematics Career Bulletin Board (Northwest hallway, fourth floor, McBryde Hall), at the Career Services office, on Internet, and the interview schedule can also be purchased at Kinkos, e.g., dates for interviews, resumé drops, priority sign-ups, and open sign-ups.

In the present economic climate, most jobs are found by directly contacting companies; even ones who are not interviewing on campus or ones who do not say they will interview mathematics majors. Talk to a career a advisor or the Career Services office about the best ways to make these contacts. IMPORTANT: Be sure that you never attend an interview without being fully informed about the company/agency and its work.

If you plan to go to graduate school, you should make preliminary inquiries about graduate schools before the end of your junior year. (Again see our departmental career Web site.) Also talk to professors that may have attended the graduate school in which you are interested, and consult the graduate catalogs on the third floor of the library.) At the beginning of your senior year, you should start writing for application forms, both for admission and for financial aid. Many graduate schools require the Graduate Record Examination. Plan to take it in October of your senior year. Finally, allow enough time for professors to write your letters of reference.

You may wish to consider graduate work in a field other than mathematics; probably in the area of your applied concentration. One need not have a B.S. in a discipline in order to do graduate work in that area. There will, of course, be certain basic courses that you will be expected to have had. You or your advisor can easily check with the other discipline about these courses.

Some of the general areas where majors in mathematics find employment are listed below. After each title, some courses which should help you in the area are listed. Additional information about employment can be found in the handbook on Mathematical Careers or from a career advisor.

Actuarial Science

Include courses in probability and statistics (Stat 4105-6 or 4705-6 are good choices), economics (Econ 2115-6), accounting (ACIS 2004, or ACIS 2115-6), and perhaps a course in finance.

Business

Include the same courses as for actuarial science, with perhaps less emphasis on statistics and more on economics. Business Law (FIN 3055-6) is a nice elective for a career in business.

Operations Research

Include courses in probability and statistics (Stat 4105-6 or 4705-6), computer science (at least CS 1014, 1044, 1104, and 1704), operations research (IEOR 3204, 3405, and 3406), and numerical analysis (Math 4445-6).

Statistics

Take theoretical statistics (Stat 4105-6) and choose from specific areas. A statistics minor would be valuable.

Computer Science

Take CS 1044, 1104, 1704, 2304, 2504, and 2604, and choose from specific computer science areas. A computer science minor would be valuable.

Finance

Take ACIS 2004, FIN 3104, FIN 4164, and FIN 4174. Other recommended courses are ECON 2115-2116, FIN 4114, FIN 4124, and FIN 4144. The Finance courses rely on a statistical foundation such as is found in STAT 2004 or 3104.

Checksheet for the Traditional Option

MATHEMATICS GUIDE SHEET FOR THE TRADITIONAL OPTION

MATHEMATICS COURSES

1. Twelve semester hours must be 4000-level. (Any 5000-level Mathematics course may be substituted for a 4000-level course.)
2. Not more than one course is allowed from 4044, 4334, and 4344.
3. A sequence or cluster must be completed from one of the following two-course sets:
   
   [4225-6]; [4245-6]; [4325-6]; [4425-6]; [4445-6]; [4124, 4134]; [4124, 4164]; [4124, 5114]; [4134, 4164]; [4214, 4225]; [4214; 4425]; [4225, 4234]; [4245, 4254]; [4245, 4454]; [4245, 4425]; [4414, 4445]; [4414, 4446]; [5454, 5464].

ADVICE

Pass-Fail: All courses taken under the headings I, II, and III must be taken for grade.

Heading I: A grade of C or better in each of 1114, 1205-1206, 1224, and either 2214 or 2224 is required (or a 2.2 QCA in these courses with no worse than one C-) before enrollment in 3034.

Twelve hours, not including 3144 or 4145, are required. Six of these hours must come from a sequence or cluster listed on the Mathematics Guide Sheet. (Either [3144, 4144] or [4145-6] counts as a sequence, but neither 3144 nor 4145 counts towards these 12 hours.) Not more than one course is allowed from 4044, 4334, and 4344.

Math 4544 may be automatically substituted for either 2214.

Heading II: Math-related courses are (a) fundamental to a discipline that uses a significant amount of advanced mathematics and (b) courses that use mathematical constructions or concepts that are at least as sophisticated as freshman calculus. A list of approved courses is given on page 10.

One of CS 1014, 1034, 1044, 1104, 1704, or 1705 is required. This course also counts as part of the 16 mathematics-related hours in Heading II.

Heading III:

Area 1. The appropriate freshman English placement is done automatically by the Director of Freshman English.

Foreign Language. Proficiency equivalent to one year of university instruction must be demonstrated in one foreign language. High school language III (e.g. German III) or a sufficient score on a placement test or achievement test will satisfy this requirement.

Courses in core categories must come from the approved lists given earlier in this handbook.

Heading IV: There are at least 26 hours of electives; usually more if departmental and college requirements are combined. The Mathematics Department recommends more mathematics courses than the minimum number (but more than 60 hours is not permitted) or, more math-related courses.