Handbook for Undergraduate
Mathematics Majors
Department of Mathematics and Statistics
Penn State Altoona
math.aa.psu.edu/degrees
September 2008
.
i
Contents
Chapter 1
Introduction
Welcome to the Penn State Altoona Mathematics Program. We hope your experience as a Mathematics Major is a rewarding one. Mathematics is not only a fascinating subject of great intrinsic
beauty, its wide applicability to the natural and social sciences is also universally recognized. Penn
State Altoona offers two degree programs: the B.A. degree and the B.S. degree. Our curriculum
emphasizes the development of analytical skills and independent thinking which is vital in an everchanging world.
In this handbook, we give an overview of the various options available within the Mathematics
Program and their course requirements. When planning your program of studies, use the sample
schedules and check sheets in this handbook together with information available online (Department
of Mathematics and Statistics at math.aa.psu.edu; online advising service at www.elion.psu.edu;
undergraduate degree bulletin at www.psu.edu/bulletins/bluebook), and consult your academic adviser. For more information about anything pertaining to the Undergraduate Mathematics Program,
please consult the Mathematics Degree Coordinator (Karl Lorensen, kql3@psu.edu).
Entrance to Mathematics Major
Students enrolled at Penn State as provisional/nondegree students may be admitted to the Mathematics Majors (MTAAL and MTSAL) if they have a cumulative GPA of at least 2.0 and they have
earned a grade of C or better in both Math 140 and Math 141. Students with advanced standing
from other academic institutions may be admitted to the Mathematics Majors (MTAAL and MTSAL) if they have a cumulative GPA of at least 2.5, they have taken 8 credits of Calculus with
1
2
1. Introduction
Analytic Geometry (equivalent to Math 140/141), and they have earned a grade of C or better in
each of these Calculus courses.
Special Options within the Major
Penn State Altoona offers two options under the B.S. Degree program; the General Option and the
Systems Analysis Option. Which option you choose depends on your strengths and interests, as
well as your career plans. These options differ only in the junior and senior years. This means that
you can put off the choice of an option until as late as your fifth semester. If possible, it should
not be made much later. Descriptions of the two options are given later in this handbook. You are
encouraged to talk to your advisor before making a decision.
Areas of Application
The Systems Analysis Option under the B.S. Degree Program requires “an approved sequence in
an area of application.” Choosing these courses should not be taken lightly. In this option you are
preparing to apply mathematics to solving problems in specific areas outside mathematics. This
means that you must learn both the mathematics relevant to those areas and enough of the area
of application to be able to communicate with the experts in that area. The courses chosen should
form a coherent pattern and should include one or two 400-level courses. Be sure to have your
course selections approved, in writing, by your advisor and a copy placed in your file in the Degree
Coordinator’s Office (Karl Lorensen, 111 Hawthorn).
The General Option under the B .S. Degree Program requires a sequence of courses in mathematics, or related area, or an area of application. The same guidelines apply here as with the
Systems Analysis Option.
Supporting Courses
These are optional courses that students can select. You can use these courses to fulfill minor
requirements in another subject. For restrictions, see Appendix C.
General Education
Every student has to take 45 credits of General Education courses. The course selections are designed to provide you with a well-rounded academic experience within an integrated curriculum
that allows for individual flexibility. General Education courses may be relevant to your major
or to your particular interests. The Baccalaureate Degree General Education Program consists
Honors Courses and the University Scholars Program
3
of two components: (1) Skills and (2) Knowledge Domains for a total of 45 credits. The Skills
component includes: Writing/Speaking (9 credits) and Quantification (6 credits). The Knowledge
Domains include: Health and Physical Activity (3 credits), Natural Science (9 credits), Arts (6
credits), Humanities (6 credits) and Social and Behavioral Sciences (6 credits). For a complete
listing of all approved courses in the Skills and Knowledge Domains, please refer to the web site:
http://www.psu.edu/bulletins/bluebook/gened/.
Concurrent Majors
A candidate receiving approval from the colleges involved may gain entrance to more than one major.
The idea of majoring in two areas in order to broaden one’s knowledge is a good one, but such a program requires ability and diligence. Anyone interested in taking on a second major should first speak
with the Degree Coordinators of both of the degree programs. The candidate successfully completing
the requirements for multiple majors will receive a separate diploma for each major for which requirements have been completed. The final academic record will indicate the completion of the requirements for each major. For more information see http://www.psu.edu/dus/handbook/concurrent.html.
Minor Degrees in other Disciplines
Mathematics majors are encouraged to pursue minors in fields outside of mathematics. The interdisciplinary nature of the mathematical sciences allows for combining and integrating many different
subjects within the mathematics B.A. and B.S. programs. The selection of courses for the “area of
application” and “supporting courses” of the mathematics majors can be done to simultaneously
fulfill the requirements for minors in other subjects. For a listing of available minors, visit the web
site: www.altoona.psu.edu.
Honors Courses and the University Scholars
Program
Several hundred of the most talented Penn State Undergraduates are in the University Scholars
Program. For incoming Freshmen, admission to this program is by a separate application reviewed
by the Faculty Selection Committee. For students already here, admission to the program is on the
basis of cumulative grade point average or, in some cases, by faculty nomination. To graduate in the
program, a student must maintain a high average every semester, take a certain minimum number
of credits in courses with an Honors designation, and write an Honors Thesis. More information
about the Scholars Program is available at the Program Office in 10 Schreyer Honors College or at:
www.scholars.psu.edu. The Department of Mathematics and Statistics teaches Honors sections of
4
1. Introduction
several courses. It is possible for a student not in the Scholars Program to enroll in Honors sections.
For more information, see the Mathematics Degree Coordinator (Karl Lorensen, kql3@psu.edu) or
the Coordinator for the Department of Mathematics and Statistics.
Evaluation of Courses from Other Universities
Each student who applies for courses to be transferred to Penn State is required to have a transcript
sent to the Office of Admissions, where the Admissions staff evaluates it. When a course taken
elsewhere is believed equivalent to a course given at Penn State, credit for that specific Penn State
course is assigned and an entry made in the “Number” column. If such a correspondence cannot
be made, general credits (denoted “GEN” in the “Credits” column) are assigned as appropriate.
The general credit designation does not imply that the credits cannot be transferred, but merely
that the Office of Admissions is unable to establish the degree of overlap between a course taken
elsewhere and a course offered here. The general credit designation implies that the student has the
responsibility for obtaining assessments of course equivalences “as appropriate.” The determination
of “appropriateness” is left to the individual colleges. For the Altoona College, the policy depends
on the type of course for which general credit has been assigned.
(1) General credit assigned for non-science or non-mathematically oriented courses (arts, social
sciences, humanities, etc.) – no need for assessment. If, for example, you have been granted
3 credits for a course in Political Science, Penn State Altoona will accept that course as
fulfilling 3 of the 6 credits to be completed in the General Education area of Social &
Behavorial Sciences. You will not be required to establish the identity of the equivalent
course offered at Penn State.
(2) General credit assigned for science or mathematically oriented courses – obtain assessments from the appropriate department coordinators: Biology, Chemistry, Earth Sciences,
Mathematics and Statistics, Physics.
Please take the course catalog of your previous institution with you. An especially careful assessment must be made of your science/mathematics background because courses in this science and
mathematics are almost always sequential, appropriate placement is essential.
Cooperative Education Program
The Cooperative Education Program gives students a chance to integrate their academics with
relevant workplace experience. Students gain an understanding of how to apply their learning
experience in an academic and non academic setting. Requirements to participate in a mathematics
co-op are: a cumulative grade-point average of 2.0 or above and completion of 30 credits. Note:
Careers for Mathematics Graduates
5
some companies may request more stringent requirements. For further information on The Eberly
College of Science Cooperative Education Program contact: Co-op@thunder.science.psu.edu or (814)
865-5000, FAX (814) 863-8466 Web: www.science.psu.edu/coop/.
MASS Program
MASS is a semester-long program that provides a comprehensive mathematical environment for a
group of talented undergraduate students selected from colleges and universities across the country.
The program combines advanced learning with research initiation. Web: www.math.psu.edu/mass
Careers for Mathematics Graduates
Since mathematical knowledge and abilities are inherent in a broad range of industries and professions, a mathematics degree is a versatile and respected credential to have when you begin looking
at career options. For information about careers for Mathematics graduates, you are strongly encouraged to visit the following web sites:
www.ams.org/employment/undergrad.html
www.awm-math.org/career.html
www.beanactuary.org
www.maa.org/careers/index.html
www.siam.org
math.aa.psu.edu/degrees
6
1. Introduction
Chapter 2
Bachelor of Arts Degree
in Mathematics
This degree program is intended for students whose interests outside mathematics are oriented
toward the arts, humanities and social sciences. The requirements in these areas are greater than
for the B.S. degree (See Appendix D).
Students in this degree program are strongly encouraged to select an area where mathematics is
applied. These courses can be used as Supporting Courses. Areas similar to those in the B.S. degree
can be used.
The only courses in this degree, which can be scheduled under the satisfactory/unsatisfactory option,
are supporting courses (Appendix C of this Handbook).
7
8
2. Bachelor of Arts Degree in Mathematics
Bachelor of Arts Check Sheets (120 credits)
1 MAJOR REQUIREMENTS (41–43 credits)
MATH 140* (4)
Choose 3 Credits Below:
MATH 141* (4)
CSE 121 (3)
OR
MATH 411* (3)
OR
CMPSC 101 (3)
OR
MATH 412* (3)
OR
CMPSC 201C (3)
MATH 417* (3)
OR
MATH 220 (2)
MATH 419* (3)
OR
MATH 230 (4)
MATH 421* (3)
MATH 250 (3)
OR
MATH 251 (4)
Choose 6 credits of 400-level MATH
MATH 311W* (3)
Except: MATH 401, 405, 406, 441, 470, and 471.
MATH 312* (3)
MATH 403* (3)
MATH
* (3)
MATH 435* (3)
OR
MATH
* (3)
MATH 436* (3)
Total Credits:
Note: Requirements indicated with * identify courses that require a minimum grade of ‘C’ for
graduation.
2 BACHELOR OF ARTS REQUIREMENTS (38–39 credits)
FOREIGN LANGUAGE (12):
ARTS (3 CR)
LEVEL I:
(4)
LEVEL II:
(4)
( )
LEVEL III:
(4)
HUMANITIES (3 CR)
OTHER CULTURES (3 CR):
( )
( )
SOC./BEHAV. SCI
(3 CR)
( )
Total Credits:
SUPPORTING
COURSES (14–15)
(
(
(
(
(
(
(
)
)
)
)
)
)
)
Bachelor of Arts Check Sheets (120 credits)
9
Foreign Language - Proficiency in a single foreign language equivalent to completion of three semesters
of course work must be demonstrated. If fewer than 12 credits are needed to reach this level of proficiency, then choose courses from the Supporting Courses List (Appendix C in the Degree Handbook)
to total 12 credits. Policies regarding placement in a foreign language can be found in Appendix A
of the Degree Handbook.
Bachelor of Arts Requirements - choose 3 credits from the Arts, 3 credits from the Humanities, 3
credits from Social/Behavioral and 3 credits from the Other Cultures lists in Appendix D of the
Degree Handbook.
Note: Other Cultures courses do not double count as US/IL courses.
Supporting Courses - A list of supporting courses is in Appendix C in the Degree Handbook.
10
2. Bachelor of Arts Degree in Mathematics
3 GENERAL EDUCATION (40 credits)
ENGL 15 OR 30 (3)
(GWS) ARTS (6 CR) (GA)
ENGL 202 (3)
(GWS)
( )
CAS 100 (3)
(GWS)
( )
NATURAL SCI. (9 CR) (GN)
( )
( )
HUMANITIES (6 CR) (GH)
( )
( )
( )
( )
( )
( )
( )
US CULTURES (3 CR) (US)
WRITING ACROSS THE
CURR.
INT’L CULTURES (3 CR) (IL)
SOC./BEHAV.SCI (6CR) (GS)
( )
( )
( )
HEALTH/PHYS. ACT.
(3 CR) (GHA)
( )
( )
( )
FIRST-YEAR
SEMINAR
(1)
Total Credits:
General Education Courses - a description of these requirements can be found at
www.psu.edu/bulletins/bluebook/gened.
Note: A student may, in consultation with the advisor and the student’s college dean, develop a
sequence of 9 credits in either the arts, humanities, or social or behavioral sciences by substituting
3 credits from one of the other two areas not in the student’s major field of study.
US Cultures and International Cultures Requirements - Students must complete a 3-credit course
in United States Cultures (US) and a 3-credit course in International Cultures (IL).
See www.psu.edu/bulletins/bluebook/gened.
4 REMEDIAL &
REPEATED COURSES
6 CREDITS
5 SENATE POLICY 83-80
Courses that do not meet
degree requirements:
Total Credits Earned:
Source/Time for credit acquisition:
(less repeats and remedial;
must have at least 120)
36 of the last 60 credits at PSU?
60 credits in the last 5 years?
Grand Total Credits:
(MUST HAVE AT LEAST 120 CREDITS TO GRADUATE.)
Bachelor of Arts Course Schedule
11
Bachelor of Arts Course Schedule
First Semester:
Math 140
Natural Science
Foreign Language I
Arts, Humanities or Soc. Sci.
First-Year Seminar
Total Semester Credits
Third Semester:
Math 220
Math 230
Foreign Language III
Natural Science
Arts, Humanities or Soc. Sci.
Total Semester Credits
Fifth Semester:
Second Semester:
4
3
4
3
1
15
2
4
4
3
3
16
Math 141
Natural Science
Foreign Language II
English 15
Health/Physical Activity
Total Semester Credits
Fourth Semester:
Math 250 or 251
Math 311W
CSE 121 or CMPSC 201C
CAS 100
Health/Physical Activity
Total Semester Credits
Sixth Semester:
4
3
4
3
1.5
15.5
3 or 4
3
3
3
1.5
13.5–14.5
Math 312
3
Math 435 or Math 436
3
Supporting Course
3 or 4
Other Cultures
3
Arts, Humanities or Soc. Sci.
3
Math 403
400-Level Math**
Supporting Course
English 202C
Arts, Humanities or Soc. Sci.
3
3
3 or 4
3
3
Total Semester Credits
Seventh Semester:
Total Semester Credits
Eighth Semester:
15–16
400-Level Math*
3
Supporting Course
3 or 4
Other Cultures
3
Arts, Humanities or Soc. Sci.
3
Arts, Humanities or Soc. Sci.
3
Arts, Humanities or Soc. Sci.
3
400-Level Math**
Supporting Course
English 202C
Arts, Humanities or Soc. Sci.
Arts, Humanities or Soc. Sci.
3
3 or 4
3
3
3
Total Semester Credits
Total Semester Credits
12–13
15–16
15–16
A minimum of 120 credits is required to graduate.
Courses in bold require a minimum grade of ‘C’ for graduation.
*Choose 3 credits from Math 411, 412, 417, 419, 421.
**Any 400-level Math except Math 401, 405, 406, 441, 470, or 471.
12
2. Bachelor of Arts Degree in Mathematics
Chapter 3
Bachelor of Science
Degree in Mathematics
(General Option)
The purpose of this option is to provide a way for students to construct, within limits, their own
curricula. It thus allows room in the major for a student interested in an unusual area of application
or one with an unusual range of interests within mathematics. The option requires at least one course
at the 400 level in each of the areas of analysis, algebra, and applied mathematics. An approved
sequence of 12 credits is required which may consist of courses either in mathematics or in a related
area, or in an area of application.
General Option Check Sheets (120 credits)
1 MAJOR REQUIREMENTS (26–27 credits)
MATH 140* (4)
CSE 121 (3)
OR
MATH 230 (4)
MATH 141* (4)
CMPSC 101 (3)
OR MATH 250 (3)
MATH 220 (2)
CMPSC 201C (3)
MATH 251 (4)
MATH 311W* (3)
OR
MATH 312* (3)
Total Credits:
13
14
3. Bachelor of Science Degree in Mathematics (General Option)
2 OPTION REQUIREMENTS (53–54 credits)
MATH 403*(3)
CHOOSE 6 CREDITS of 400-LEVEL MATH
CHOOSE 3 CREDITS OF: EXCEPT: MATH 401, 405, 406, 441, 470
MATH 414*(3)
OR
and 471.
MATH 418*(3)
MATH
*(3)
CHOOSE 3 CREDITS OF MATH
*(3)
MATH 435*(3)
OR
FOREIGN LANGUAGE (8):
MATH 436*(3)
LEVEL I:
(4)
CHOOSE 3 CREDITS OF: LEVEL II:
(4)
MATH 411*(3)
OR
AREA OF APPLICATION (12):
MATH 412*(3)
OR
( )
MATH 417*(3)
OR
( )
MATH 419*(3)
OR
( )
MATH 421*(3)
( )
SUPPORTING
COURSES (15–16)
(
(
(
(
(
(
(
)
)
)
)
)
)
)
Total Credits:
Foreign Language - Proficiency in a single foreign language equivalent to completion of two semesters
of course work must be demonstrated. If fewer than 8 credits are needed to reach this level of proficiency, then choose courses from the Supporting Courses List (Appendix C in the Degree Handbook)
to total 8 credits. Policies regarding placement in a foreign language can be found in Appendix A
of the Degree Handbook.
Application Area - Choose an approved sequence of 12 credits in an area of application, have it
approved by your advisor and then file a copy with the Mathematics Degree Coordinator (Karl
Lorensen, kql3@psu.edu).
Supporting Courses A list of supporting courses is in Appendix C in the Degree Handbook. The
only courses in this degree which can be scheduled under the satisfactory/unsatisfactory option are
supporting courses.
Note: Requirements indicated with * identify courses that require a minimum grade of ‘C’ for
graduation.
General Option Check Sheets (120 credits)
15
3 GENERAL EDUCATION (40 credits)
ENGL 15 OR 30 (3)
(GWS) ARTS (6 CR) (GA)
ENGL 202 (3)
(GWS)
( )
CAS 100 (3)
(GWS)
( )
NATURAL SCI. (9 CR) (GN)
( )
( )
HUMANITIES (6 CR) (GH)
( )
( )
( )
( )
( )
( )
( )
US CULTURES (3 CR) (US)
WRITING ACROSS THE
CURR.
INT’L CULTURES (3 CR) (IL)
SOC./BEHAV.SCI (6CR) (GS)
( )
( )
( )
HEALTH/PHYS. ACT.
(3 CR) (GHA)
( )
( )
( )
FIRST-YEAR
SEMINAR
(1)
Total Credits:
General Education Courses - a description of these requirements can be found at
www.psu.edu/bulletins/bluebook/gened.
Note: A student may, in consultation with the advisor and the student’s college dean, develop a
sequence of 9 credits in either the arts, humanities, or social or behavioral sciences by substituting
3 credits from one of the other two areas not in the student’s major field of study.
US Cultures and International Cultures Requirements - Students must complete a 3-credit course
in United States Cultures (US) and a 3-credit course in International Cultures (IL).
See www.psu.edu/bulletins/bluebook/gened.
4 REMEDIAL &
REPEATED COURSES
6 CREDITS
5 SENATE POLICY 83-80
Courses that do not meet
degree requirements:
Total Credits Earned:
Source/Time for credit acquisition:
(less repeats and remedial;
must have at least 120)
36 of the last 60 credits at PSU?
60 credits in the last 5 years?
Grand Total Credits:
(MUST HAVE AT LEAST 120 CREDITS TO GRADUATE.)
16
3. Bachelor of Science Degree in Mathematics (General Option)
General Mathematics Option Course Schedule
First Semester:
Math 140
Natural Science
Foreign Language I
Arts, Humanities or Soc. Sci.
First-Year Seminar
Total Semester Credits
Third Semester:
Math 220
Math 230
CAS 100
Natural Science
Arts, Humanities or Soc. Sci.
Total Semester Credits
Fifth Semester:
Second Semester:
4
3
4
3
1
15
2
4
3
3
3
15
Math 141
Natural Science
Foreign Language II
English 15
Health/Physical Activity
Total Semester Credits
Fourth Semester:
Math 250 or 251
Math 311W
CSE 121 or CMPSC 201C
English 202C
Health/Physical Activity
Total Semester Credits
Sixth Semester:
4
3
4
3
1.5
15.5
3 or 4
3
3
3
1.5
13.5–14.5
Math 312
3
Math 435 or Math 436
3
Application Area Course
3
Supporting Course
3 or 4
Arts, Humanities or Soc. Sci.
3
Math 403
Math 414
Application Area Course
Supporting Course
Arts, Humanities or Soc. Sci.
3
3
3
3 or 4
3
Total Semester Credits
Seventh Semester:
Total Semester Credits
Eighth Semester:
15–16
400-Level Math*
3
400-Level Math**
3
Application Area Course
3
Supporting Course
3 or 4
Arts, Humanities or Soc. Sci.
3
400-Level Math**
Application Area Course
Supporting Course
Arts, Humanities or Soc. Sci.
3
3
3 or 4
3
Total Semester Credits
Total Semester Credits
12–13
15–16
15–16
A minimum of 120 credits is required to graduate.
Courses in bold require a minumum grade of ‘C’ for graduation.
*Choose 3 credits from Math 411, 412, 417, 419, 421.
**Any 400-level Math except Math 401, 405, 406, 441, 470, or 471.
Recommended supporting courses include: CSE 122, CSE 271, and CSE 275.
Chapter 4
Bachelor of Science
Degree in Mathematics
(Systems Analysis
Option)
The intent of this option is to train people to apply mathematics toward the solution of problems in
business, economics, and the social and behavioral sciences. The main mathematical tools needed are
matrix theory, linear programming, and statistics. The requirements include an approved sequence of
courses in an area of application (see Appendix F in the Degree Handbook for suggested sequences).
Systems Analysis Option Check Sheets (120
credits)
1 MAJOR REQUIREMENTS (26–28 credits)
MATH 140* (4)
CSE 121 (3)
OR
MATH 230 (4)
MATH 141* (4)
CMPSC 101 (3)
OR MATH 250 (3)
MATH 220 (2)
CMPSC 201C (3)
MATH 251 (4)
MATH 311W* (3)
OR
MATH 312* (3)
Total Credits:
17
18
4. Bachelor of Science Degree in Mathematics (Systems Analysis Option)
2 OPTION REQUIREMENTS (53–54 credits)
MATH 414*(3)
CHOOSE 3 CREDITS of 400-LEVEL MATH
MATH 415*(3)
EXCEPT: MATH 401, 405, 406, 441, 470
MATH 436*(3)
and 471.
MATH 484*(3)
MATH
*(3)
FOREIGN LANGUAGE (8):
CHOOSE 6 CREDITS OF: LEVEL I:
(4)
LEVEL II:
(4)
MATH 310*(3)
OR
AREA OF APPLICATION (12):
MATH 451*(3)
OR
( )
MATH 485*(3)
OR
( )
MATH 486*(3)
OR
( )
( )
SUPPORTING
COURSES (12–13)
(
(
(
(
(
(
(
)
)
)
)
)
)
)
Total Credits:
Foreign Language - Proficiency in a single foreign language equivalent to completion of two semesters
of course work must be demonstrated. If fewer than 8 credits are needed to reach this level of proficiency, then choose courses from the Supporting Courses List (Appendix C in the Degree Handbook)
to total 8 credits. Policies regarding placement in a foreign language can be found in Appendix A
of the Degree Handbook.
Application Area - Choose an approved sequence of 12 credits in an area of application, have it
approved by your advisor and then file a copy with the Mathematics Degree Coordinator (Dr.
David Hurtubise, Hurtubise@psu.edu).
Supporting Courses A list of supporting courses is in Appendix C in the Degree Handbook. The
only courses in this degree which can be scheduled under the satisfactory/unsatisfactory option are
supporting courses.
Note: Requirements indicated with * identify courses that require a minimum grade of C for graduation.
Systems Analysis Option Check Sheets (120 credits)
3 GENERAL EDUCATION (40 credits)
ENGL 15 OR 30 (3)
(GWS) ARTS (6 CR) (GA)
ENGL 202 (3)
(GWS)
( )
CAS 100 (3)
(GWS)
( )
NATURAL SCI. (9 CR) (GN)
( )
( )
HUMANITIES (6 CR) (GH)
( )
( )
( )
( )
( )
( )
( )
US CULTURES (3 CR) (US)
WRITING ACROSS THE
CURR.
INT’L CULTURES (3 CR) (IL)
19
SOC./BEHAV.SCI (6CR) (GS)
( )
( )
( )
HEALTH/PHYS. ACT.
(3 CR) (GHA)
( )
( )
( )
FIRST-YEAR
SEMINAR
(1)
Total Credits:
General Education Courses - a description of these requirements can be found at
www.psu.edu/bulletins/bluebook/gened.
Note: A student may, in consultation with the advisor and the student’s college dean, develop a
sequence of 9 credits in either the arts, humanities, or social or behavioral sciences by substituting
3 credits from one of the other two areas not in the student’s major field of study.
US Cultures and International Cultures Requirements - Students must complete a 3-credit course
in United States Cultures (US) and a 3-credit course in International Cultures (IL).
See www.psu.edu/bulletins/bluebook/gened.
4 REMEDIAL &
REPEATED COURSES
6 CREDITS
5 SENATE POLICY 83-80
Courses that do not meet
degree requirements:
Total Credits Earned:
Source/Time for credit acquisition:
(less repeats and remedial;
must have at least 120)
36 of the last 60 credits at PSU?
60 credits in the last 5 years?
Grand Total Credits:
(MUST HAVE AT LEAST 120 CREDITS TO GRADUATE.)
20
4. Bachelor of Science Degree in Mathematics (Systems Analysis Option)
Systems Analysis Option Course Schedule
First Semester:
Math 140
Natural Science
Foreign Language I
Arts, Humanities or Soc. Sci.
First-Year Seminar
Total Semester Credits
Third Semester:
Math 220
Math 230
CAS 100
Natural Science
Arts, Humanities or Soc. Sci.
Total Semester Credits
Fifth Semester:
Second Semester:
4
3
4
3
1
15
2
4
3
3
3
15
Math 141
Natural Science
Foreign Language II
English 15
Health/Physical Activity
Total Semester Credits
Fourth Semester:
Math 250 or 251
Math 311W
CSE 121 or CMPSC 201C
English 202C
Health/Physical Activity
Total Semester Credits
Sixth Semester:
4
3
4
3
1.5
15.5
3 or 4
3
3
3
1.5
13.5–14.5
Math 312
3
Math 436 or Math 484
3
Application Area Course
3
Supporting Course
3 or 4
Arts, Humanities or Soc. Sci.
3
300 or 400-Level Math*
Math 414
Application Area Course
Supporting Course
Arts, Humanities or Soc. Sci.
3
3
3
3 or 4
3
Total Semester Credits
Seventh Semester:
Total Semester Credits
Eighth Semester:
15–16
15–16
Math 415
3
Math 484 or 436
3
Application Area Course
3
Supporting Course
3 or 4
Arts, Humanities or Soc. Sci.
3
300 or 400-Level Math*
400-Level Math**
Application Area Course
Arts, Humanities or Soc. Sci.
Total Semester Credits
Total Semester Credits
15–16
A minimum of 120 credits is required to graduate.
Courses in bold require a minumum grade of ‘C’ for graduation.
*Choose 6 credits from Math 310, 451, 485, 486.
**Any 400-level Math except Math 401, 405, 406, 441, 470, or 471.
Recommended supporting courses include: CSE 122, CSE 271, and CSE 275.
3
3
3
3
12
Chapter 5
Minors in Mathematics
Mathematics Minor
Students must take MATH 140 GQ(4), 141 GQ(4); select 6-8 credits from MATH 220 GQ(2), 230(4),
231(2), 232(2), 250(3), 251(4), 310(3), 311W(3), or 312(3); and select 12 credits of 400-level MATH
courses. A total of 26-28 credits is required for the minor. For successful completion of the minor a
candidate must receive a grade of ‘C’ or better in each of the four 400-level courses.
Mathematics Applications Minor
Students must take MATH 140 GQ(4), 141 GQ(4); select 6-8 credits from MATH 220 GQ(2), 230(4),
231(2), 232(2), 250(3), 251(4), 310(3), 311W(3), or 312(3); and select 6 credits from 400-level MATH
courses and 6 credits from Mathematics Applications courses*. A total of 26-28 credits is required
for the minor. For successful completion of the minor a candidate must receive a grade of ‘C’ or
better in each of the four 400-level courses.
*Through consultation with the coordinator of the minor, courses from areas that directly incorporate or support the use of mathematics will be selected. Typical areas include computer science,
engineering, physics, and statistics. Acceptable mathematics applications courses include (but are
not limited to) the following:
Any 400-level MATH course
Any 400-level STAT course
ASTRO 440
CHEM 408, 451-463
CSE 451-457,460-468,477,485,486
E E 411-414,418-461,485-492
EMET 430, 440
M E 403-476
NUC E 401-490
PHYS 400-443, 461
21
Appendix A
Foreign Language
All students interested in scheduling a foreign language at Penn State may choose either to continue
the language they began in high school or to begin a new one. To continue with a language, students
must follow the placement policy as outlined below.
Placement Policy
Students who have studied a foreign language in grades 9 through 12 within four years immediately
before admission to Penn State may only enroll in that language for credit based on the number of
units of high school work completed.
Register in
Units of Study, Grades 9-12
Fewer than two
Course Level 001 (4 crs.)
Two or three
Course Level 002 (4 crs.)
Four or more
Course Level 003 (4 crs.)
Students may choose to audit a lower-level course but may not receive credit for it. Students who
feel they are qualified for a more advanced course will be offered a diagnostic examination a few
days after the beginning of each semester.
Non-Coursework Knowledge of Foreign
Languages
Students who have acquired a knowledge of a foreign language by means other then coursework (e.g.,
family background, travel or study in a foreign country, participation in non-credit summer language
institutes, etc.) may enroll in elementary and intermediate courses in that language only with the
permission of the course coordinator or department coordinator. Students whose native language
23
24
A. Foreign Language
is something other than English may not receive credit (through coursework or examination) for
elementary and intermediate courses in their native language. Enrollment in skills courses beyond
intermediate level (e.g., conversation, composition) must be approved by the department coordinator.
Intensive courses
Students may choose to enroll in intensive courses –French 111 and 112, Spanish 10 and 20, or
Summer Intensive Language Institute courses. Because the objectives of these intensive courses are
somewhat different, students may schedule them for full credit even if they have studied the language
previously.
Credit by Examination/Proficiency Examination
(Senate Policy 42-50)
Credit by Examination (graded, fee charged) and Credit by Undergraduate Proficiency Examination
(ungraded, no fee) are available to the extent allowed by this policy. For example, a student who
has two units of high school foreign language and chooses to begin study of that language at the
third level instead of the second (Course Level 003, 4 cr.), may receive credits for the second level
(Course Level 002, 4 cr.), but not for the first level (course Level 001, 4 cr.).
Questions
Questions should be addressed to the course coordinator or department coordinator of the particular
language department concerned.
Appendix B
Statistics Courses for
Mathematics Majors
The following is a description of statistics courses, which may be of interest to undergraduate mathematics majors. With the exception of STAT 220, courses numbered below 414 should not be
considered by most mathematics majors.
STAT 220
STAT 220 is an elementary applied statistics course which shows students how statistics is used in
the real world. This is a good course to take before the sequence Math 414-415 which covers the
theory of probability and statistics.
STAT (Math) 414-415
A two semester sequence in probability and mathematical statistics. This sequence is the one which
the Statistics Department most strongly recommends for mathematics majors interested in statistics.
It develops the basic theory of probability and statistics.
STAT (Math) 416
A one-semester course in stochastic modeling (applied probability). An excellent course for mathematics majors interested in probability.
STAT (Math) 418
A one-semester course in probability. An excellent course for mathematics majors interested in
probability but not statistics.
Note: STAT (Math) 414 and STAT (Math) 418 cover very similar material but from different
perspectives. STAT 414 is intended to lead to the study of statistics and STAT 418 is intended as
25
26
B. Statistics Courses for Mathematics Majors
a course in probability alone. Students do not get credit for both 414 and 418. STAT 418 is an
adequate prerequisite for STAT 415, although students who plan to take STAT 415 would be better
advised to take STAT 414 than STAT 418. Students are permitted to substitute 414 for 418 and
vice versa in the requirements for all options.
Applied Statistics (STAT 460, 462, 464)
These courses offer students a chance to learn about common statistical techniques on a more
advanced level than seen in a course such as STAT 220 and to apply these techniques to data sets.
These courses tend to involve less theory and more computing than the probability and math STAT
courses; the goal is intelligent application of results, most of which are presented without rigorous
proof.
STAT 460 – Intermediate applied statistics. A more advanced study of a range of statistical techniques than is seen in introductory statistics classes.
STAT 462 – Applied regression analysis. An in-depth study of topics in linear regression. (STAT
462 is a highly recommended choice for Actuarial Majors to study for the actuarial examinations.)
STAT 464 – Applied nonparametric statistics. An in-depth study of tests based on nominal and
ordinal data.
Appendix C
Bachelor of Arts and
Bachelor of Science
Supporting Courses
Any Baccalaureate Degree course except:
ADTED 100
CMPSC 1, 100, 101B, 102, 110, 142, 144, 154, 164, 174, 175, 201F and 203
ENGL 4, 5
LL ED 5, 10
MATH 1, 2, 3, 4, 17, 18, 21, 22, 26, 35, 36, 40, 41, 81, 82, 83, 87, 88, and 200
MTHBD 91, 92
SPCOM 126
STAT 100 and 200
NOTE: Courses which substantially duplicate subject matter covered in other courses the student
has taken will not count toward degree requirement, e.g.: BIOL 11 and BIOL 12 if student has taken
BIOL 110 CSE 260 if student has taken Math 311W STAT 200 if student has taken STAT 250
27
28
C. Bachelor of Arts and Bachelor of Science Supporting Courses
Appendix D
Bachelor of Arts
Requirements
The Bachelor of Arts degree requires courses from the Arts (3 credits), Humanities (3 credits), Social
and Behavioral Sciences (3 credits), Other Cultures (3 credits) and Foreign Language (0-12 credits).
For a complete listing of all approved courses in the Bachelor of Arts basic requirements, please refer
to web site: www.psu.edu/bulletins/bluebook/gened/bad.html.
29
30
D. Bachelor of Arts Requirements
Appendix E
Actuarial Science
Examinations
We encourage you to download the “Basic Education Catalog” published by the Society of Actuaries
at: www.soa.org. The catalog contains a full description of the actuarial examinations: topics,
text books, schedules, locations and application forms.
Recommended 400-Level Mathematics Courses
(1) STAT 462 (This course is highly recommended to help students study for the actuarial
examinations.)
(2) Math 403
(3) Math 436
(4) Math 486
Recommended General Education Courses (Social/Behavioral Sciences)
(1) ECON 2, ECON 4
Recommended Supporting Courses
(1) ACCTG 211, FIN 204
(2) FIN 301, INS 305
(3) INS 320, INS 401
Actuarial Club web site: www.smeal.psu.edu/studorgs/actsci/index.htm
31
32
E. Actuarial Science Examinations
Appendix F
Suggested Application
Area Sequences
The General Option and the Systems Analysis Option of the B.S. Degree in Mathematics both
include a 12-credit sequence in an area of application. For the General Option these 12 credits
can be in mathematics, in a related area, or in an area of application. For the Systems Analysis
Option the sequence of courses should be in an area of application. The courses chosen should form
a coherent pattern and should include one or two 400-level courses. This sequence of courses must
be approved by the student’s advisor, and a copy should be filed with the Mathematics Degree
Coordinator (Karl Lorensen, kql3@psu.edu).
In the Systems Analysis Option, students prepare to apply mathematics to solving problems in
specific areas outside mathematics. This means that they must learn both the mathematics relevant
to those areas and at least enough of the area of application to be able to communicate with the
experts in that field. The following is a partial list of application areas and potential course sequences
for either the General Option or the Systems Analysis Option.
Accounting
For students who choose accounting as their application area, the following course sequences provide
background in the basic theory and practice of accounting.
ACCTG 211 + three courses from among ACCTG 404, 471, 472, 432.
Biology
For students who choose biology as their application area, the following course sequences provide
background in biodiversity, populations and communities, genetics, molecules and cells, evolution,
and histology.
33
34
F. Suggested Application Area Sequences
BIOL 110, 220, 230, 427
BIOL 110, 222, 223, 230, 437
Biochemistry
For students who choose biochemistry as their application area, the following course sequence provides background in organic chemistry, molecules and cells, and the structure and function of biological molecules.
CHEM 38, CHEM 39, BIOL 230, BMB 401, BMB 402
Chemistry
For students who choose chemistry as their application area, the following course sequence provides
background in organic chemistry, inorganic chemistry, physical chemistry, and chemical thermodynamics.
CHEM 038, 410, 451, 452
Criminal Justice
For students who choose criminal justice as their application area, the following course sequences
provide background in law enforcement, prosecution process, community corrections, and juvenile
justice and delinquency.
CJ 210, 220, 230, 430 or 450 or 460
CJ 210, 230, 430, 460
Economics
For students who choose economics as their application area, the following course sequence provides
background in microeconomics, macroeconomics, finance, money and banking, optimal resource
allocation, alternative control procedures, levels of environmental protection and public policy.
ECON 002, 004, 302, 351, 428
Electro-Mechanical Engineering
For students who choose electro-mechanical engineering as their application area, the following
course sequence provides background in electrical circuits, microprocessors, digital electronics, and
automated machine control technology.
EET 101, EET 114, EET 211, EMET 310, EMET 430
Finance
F. Suggested Application Area Sequences
35
For students who choose finance as their application area, the following course sequence provides
background in insurance, corporation finance, investment strategies, the valuation of corporate securities, tax regulations, and tax planning applicable for personal/business decision making.
INS 301, FIN 301, FINSV 400, FINSV 411
Health Policy and Administration
For students who choose health policy and administration as their application area, the following course sequences provide background in health services organization, insurance, health systems
management, financing health care, and marketing for health services.
HPA 101, INS 301, HPA 332, HPA 447
HPA 101, MKTG 220, HPA 332, HPA 455
Human Development and Family Studies
For students who choose human development and family studies as their application area, the following course sequence provides background in empirical inquiry in human development, leadership
and technology skills for human services professionals, and program development and administration
of human service programs. The additional recommended courses focus on particular content areas:
infants/children, adolescents, adult development, and family development.
HDFS 129, 302A, 312W, 455
Additional courses: HDFS 229, 429, or HDFS 239, 433, or HDFS 249, 445, or
HDFS 218, 418
Information Sciences and Technology
For students who choose information sciences as their application area, the following course sequence
provides background in information systems.
IST 110, 220, plus two courses from among IST 451, 454, 456.
IST 110, 220 SRA 231, IST 432.
Marketing
For students who choose marketing as their application area, the following course sequence provides
background in customer behavior, channels of distribution, promotion and pricing with emphasis on
a culturally diverse environment, public relations, and the management of marketing institutions in
distribution channels from producers to consumers.
BA 250, MKTG 220, MKTG 301, MKGT 310, MKTG 327
Physics
36
F. Suggested Application Area Sequences
For students who choose physics as their application area, the following course sequence provides
background in mechanics, electricity and magnetism, fluids and thermal physics, wave motion and
quantum physics, quantum mechanics, and solid state physics.
PHYS 211, 212, 213, 214, 237, 410, 412
F. Suggested Application Area Sequences
37
Appendix G
Course Descriptions
For a complete list of courses see The Pennsylvania State University Blue Book.
CSE 121 INTRODUCTION TO PROGRAMMING TECHNIQUES (3) Design and implementation of algorithms. Structured programming. Problem solving techniques. Introduction to
a high-level language, including arrays, procedures, and recursion. Prerequisite: 2 entrance units in
mathematics
CSE 122 INTERMEDIATE PROGRAMMING (3) Systematic programming; top-down program development, documentation, and testing. Introduction to data structures, text processing,
numerical methods, algorithm analysis, program verification. Prerequisites: CMPSC 201C or 201F
or CSE 121; Math 140.
INSURANCE (INS) 301 RISK AND INSURANCE (3) Introduction to the principles and
methods of handling business and personal risks; emphasis on insurance techniques. Prerequisite:
fourth-semester standing.
140. (GQ) CALCULUS WITH ANALYTIC GEOMETRY I (4) Functions; limits; analytic
geometry; derivatives, differentials, applications; integrals, applications. Students may take only one
course for credit from MATH 110, 140, 140A, and 140B. Prerequisites: MATH 022, 026; or MATH
040 or 041; or satisfactory performance on the mathematics proficiency examination.
141. (GQ) CALCULUS WITH ANALYTIC GEOMETRY II (4) Derivatives, integrals,
applications; sequences and series; analytic geometry; polar coordinates. Students many take only
one course for credit from MATH 141 and 141B. Prerequisite: MATH 140, 140A, or 140B.
197. SPECIAL TOPICS (1-9).
199. (GI) FOREIGN STUDIES (1-12).
39
40
G. Course Descriptions
220. (GQ) MATRICES (2) Systems of linear equations; matrix algebra; eigenvalues and eigenvectors; linear systems of differential equations. Prerequisite: MATH 110 or 140.
230. CALCULUS AND VECTOR ANALYSIS (4) Three-dimensional analytic geometry;
vectors in space; partial differentiation; double and triple integrals; integral vector calculus. Students
who have passed either MATH 231 or 232 may not schedule MATH 230 for credit. Prerequisite:
MATH 141.
231. CALCULUS OF SEVERAL VARIABLES (2) Analytic geometry in space; partial differentiation and applications. Students who have passed MATH 230 may not schedule this course.
Prerequisite: MATH 141.
232. INTEGRAL VECTOR CALCULUS (2) Multidimensional analytic geometry, double and
triple integrals; potential fields; flux; Green’s, divergence and Stokes’ theorems. Students who have
passed MATH 230 may not schedule this course for credit. Prerequisite: MATH 231.
250. ORDINARY DIFFERENTIAL EQUATIONS (3) First- and second-order equations;
numerical methods; special functions; Laplace transform solutions; higher order equations. Students
who have passed MATH 251 may not schedule this course for credit. Prerequisite: MATH 141.
STAT 250. (GQ) INTRODUCTION TO BIOSTATISTICS (3) Statistical analysis and interpretation
of data in the biological sciences; probability; distributions; statistical inference for one- and twosample problems. Prerequisite: 3 credits in mathematics.
251. ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS (4) First- and secondorder equations; special functions; Laplace transform solutions; higher order equations; Fourier
series; partial differential equations. Prerequisite: MATH 141.
294. RESEARCH PROJECT (1-12).
296. INDEPENDENT STUDIES (1-18).
297. SPECIAL TOPICS (1-9).
310. ELEMENTARY COMBINATORICS (3) Fundamental techniques of enumeration and
construction of combinatorial structures, permutations, recurrences, inclusion-exclusion, permanents, 0, 1- matrices, Latin squares, combinatorial designs. Prerequisite: MATH 220.
311W. CONCEPTS OF DISCRETE MATHEMATICS (3) Introduction to mathematical
proofs; elementary number theory and group theory. Students who have passed CMPSC 260 may
not schedule this course for credit. Prerequisite: MATH 141.
312. CONCEPTS OF REAL ANALYSIS (3) An introduction to rigorous analytic proofs
involving properties of real numbers, continuity, differentiation, integration, and infinite sequences
and series. Prerequisite: MATH 141.
G. Course Descriptions
41
318. (STAT) ELEMENTARY PROBABILITY (3) Combinatorial analysis, axioms of probability,
conditional probability and independence, discrete and continuous random variables, expectation,
limit theorems, additional topics. Students who have passed either MATH (STAT) 414 or 418 may
not schedule this course for credit. Prerequisite: MATH 141.
319. (STAT) APPLIED STATISTICS IN SCIENCE (3) Statistical inference: principles and methods, estimation and testing hypotheses, regression and correlation analysis, analysis of variance,
computer analysis. Students who have passed MATH (STAT) 415 may not schedule this course for
credit. Prerequisite: MATH 318 or knowledge of basic probability.
397. SPECIAL TOPICS ( 1 - 9).
399. (GI) FOREIGN STUDIES ( 1 -12).
401. INTRODUCTION TO ANALYSIS I (3) Review of calculus, properties of real numbers, infinite
series, uniform convergence, power series. Students who have passed Math. 403 may not schedule
this course. Prerequisite: MATH 230 or MATH 231.
403. CLASSICAL ANALYSIS I (3) Topology of Rn , compactness, continuity of functions,
uniform convergence, Arzela-Ascoli theorem in the plane, Stone-Wierstrass theorem. Prerequisite:
MATH 312.
404. CLASSICAL ANALYSIS II (3) Differentiation of functions from Rn to Rm , implicit function
theorem, Riemann integration, Fubini’s theorem, Fourier analysis. Prerequisite: MATH 403.
405. ADVANCED CALCULUS FOR ENGINEERS AND SCIENTISTS I (3) Vector calculus, linear
algebra, ordinary and partial differential equations. Students who have passed MATH 411 OR 412
may not schedule this course for credit. Prerequisites: MATH 231; MATH 250 or 251.
406. ADVANCED CALCULUS FOR ENGINEERS AND SCIENTISTS II (3) Complex analytic
functions, sequences and series, residues, Fourier and Laplace transforms. Students who have passed
MATH 421 may not take this course for credit. Prerequisite: MATH 405.
411. ORDINARY DIFFERENTIAL EQUATIONS (3) Linear ordinary differential equations; existence and uniqueness questions; series solutions; special functions; eigenvalue problems; Laplace
transforms; additional topics and applications. Prerequisite: MATH 230 or MATH 231 ; MATH 250
or MATH 251.
412. FOURIER SERIES AND PARTIAL DIFFERENTIAL EQUATIONS (3) Orthogonal systems and Fourier series; derivation and classification of partial differential equations; eigenvalue function method and its applications; additional topics. Prerequisite: MATH 230 or MATH
231 ; MATH 250 or MATH 251.
42
G. Course Descriptions
414. (STAT) INTRODUCTION TO PROBABILITY THEORY (3) Probability spaces,
discrete and continuous random variables, transformations, expectations, generating functions, conditional distributions, law of large numbers, central limit theorems. Students may take only one
course from MATH (STAT) 414 and 418 for credit. Prerequisite: MATH 230 or 231.
415. (STAT) INTRODUCTION TO MATHEMATICAL STATISTICS (3) A theoretical
treatment of statistical inference, including sufficiency, estimation, testing, regression, analysis of
variance, and chi-square tests. Prerequisites: MATH (STAT) 414.
416. (STAT) STOCHASTIC MODELING (3) Review of distribution models, probability
generating functions, transforms, convolutions, Markov chains, equilibrium distributions, Poisson
process, birth and death processes, estimation. Prerequisites: MATH (STAT) 318 or 414; MATH
230.
417. QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS (3) Linear differential equations, stability of stationary solutions, ordinary bifurcation, exchange of stability, Hopf bifurcation,
stability of periodic solutions, applications. Prerequisite: MATH 220 , MATH 250.
419. (PHYS) THEORETICAL MECHANICS (3) Principles of Newtonian, Lagrangian, and
Hamiltonian mechanics of particles with applications to vibrations, rotations, orbital motion, and
collisions. Prerequisite: MATH 230 or MATH 231 ; MATH 250 or MATH 251 ; PHYS 212 , PHYS
213 , and PHYS 214 ; or PHYS 203 or PHYS 204.
420. ELEMENTARY INTRODUCTION TO CHAOTIC DYNAMICS AND FRACTAL GEOMETRY (3) An introduction to the theory of fractals for undergraduates in mathematics, science,
engineering, economics, and computer science. Prerequisite: MATH 140 , MATH 141 , MATH 220
or MATH 110 , MATH 111 , MATH 220.
421. COMPLEX ANALYSIS (3) Infinite sequences and series; algebra and geometry of complex numbers; analytic functions; integration; power series; residue calculus; conformal mapping,
applications. Prerequisites: MATH 230, 232, or 405; MATH 401 or 403.
422. WAVELETS AND FOURIER ANALYSIS: THEORY AND APPLICATIONS (3) Fundamental mathematical issues of the theory of wavelets for senior undergraduate and graduate students
in mathematics, engineering, physics, and computer science. Prerequisite: complete one of the
following: MATH 312 , MATH 401 , MATH 403 , MATH 405 , or MATH 412.
426. INTRODUCTION TO MODERN GEOMETRY (3) Plane and space curves; space surfaces;
curvature; intrinsic geometry of surfaces; Gauss-Bonnet theorem; covariant differentiation; tensor
analysis. Prerequisite: MATH 401 or 403.
427. FOUNDATIONS OF GEOMETRY (3) Euclidean and various non-Euclidean geometries and
their development from postulate systems. Prerequisite: MATH 230 or 231.
G. Course Descriptions
43
429. INTRODUCTION TO TOPOLOGY (3) Metric spaces, topological spaces, separation axioms,
product spaces, identification spaces, compactness, connectedness, fundamental group. Prerequisite:
MATH 311W.
435. BASIC ABSTRACT ALGEBRA (3) Elementary theory of groups, rings, and fields.
Prerequisite: MATH 311W.
436. LINEAR ALGEBRA (3) Vector spaces and linear transformations, canonical forms of
matrices, elementary divisors, invariant factors; applications. Prerequisite: MATH 311W.
437. ALGEBRAIC GEOMETRY (3) Study of curves in the plane defined by polynomial equations
p(x,y)= 0. Projective equivalence, singular points, classification of cubics. Prerequisite: MATH 230
or MATH 231.
441. MATRIX ALGEBRA (3) Determinants, matrices, linear equations, characteristic roots, quadratic forms, vector spaces. Students who have passed Math. 436 may not schedule this course.
Prerequisite: MATH 220.
450. MATHEMATICAL MODELING (3) Constructing mathematical models of physical phenomena; topics include pendulum motion, polymer fluids, chemical reactions, waves, flight, and chaos.
Prerequisite: MATH 405 or MATH 412.
451. (CSE) NUMERICAL COMPUTATIONS (3) Algorithms for interpolation, approximation, integration, nonlinear equations, linear systems, fast Fourier transform, and differential
equations emphasizing computational properties and implementation. Students may take only one
course for credit from MATH 451 and 455. Prerequisites: CMPSC 201C, 201F, or CSE 121; MATH
230 or 231.
455. (CSE) INTRODUCTION TO NUMERICAL ANALYSIS I (3) Floating point computation,
numerical rootfinding, interpolation, numerical quadrature, direct methods for linear systems. Students may take only one course for credit from MATH 451 and MATH 455. Prerequisite: CMPSC
201C , CMPSC 201F , or CSE 121 ; MATH 220 ; MATH 230 or MATH 231.
456. (CSE) INTRODUCTION TO NUMERICAL ANALYSIS II (3) Polynomial and piecewise
polynomial approximation, matrix least squares problems, numerical solution of eigenvalue problems,
numerical solution of ordinary differential equations. Prerequisite: MATH 455.
457. INTRODUCTION TO MATHEMATICAL LOGIC (3) Propositional logic, first-order predicate
logic, axioms and rule of inference, structures, models, definability, completeness, compactness.
Prerequisites: MATH 311W or PHIL 212; 3 additional credits in philosophy.
459. COMPUTABILITY AND UNSOLVABILITY (3) An introduction to the theory of recursive
functions; solvable and unsolvable decision problems; applications. Prerequisite: MATH 311W.
44
G. Course Descriptions
461. (PHYS) THEORETICAL MECHANICS (3) Continuation of Math.(Phys.) 419. Theoretical
treatment of dynamics of a rigid body, theory of elasticity, aggregates of particles, wave motion,
mechanics of fluids. Prerequisite: MATH 419.
465. NUMBER THEORY (3) Elements, divisibility of numbers, congruences, residues, and forms.
Prerequisite: MATH 230 or MATH 231.
467. (CSE) FACTORIZATION AND PRIMALITY TESTING (3) Prime sieves, factoring, computer
numeration systems, congruences, multiplicative functions, primitive roots, cryptography, quadratic
residues. Students who have passed MATH 465 may not schedule this course. Prerequisite: MATH
311W.
468. MATHEMATICAL CODING THEORY (3) Shannon’s theorem, block codes, linear codes,
Hamming codes, Hadamard codes, Golay codes, Reed-Muller codes, bounds on codes, cyclic codes.
Prerequisites: Math 311W; advanced calculus.
469. MATHEMATICS OF ALGORITHMS (3) Binomial identities; recurrence relations, operator
methods; asymptotic methods. Prerequisite: advanced calculus.
483. APPLIED MODERN ALGEBRA II (3) Semigroups, groups, permutation groups, machines,
Polya enumeration theory, switching functions, de Bruijn’s theorem, fast adders. Prerequisite:
MATH 311W.
484. LINEAR PROGRAMS AND RELATED PROBLEMS (3) Introduction to theory and
applications of linear programming; the simplex algorithm and new methods of solution; duality
theory. Prerequisites: MATH 220; MATH 230 or 231.
485. GRAPH THEORY (3) Introduction to the theory and applications of graphs and directed
graphs. Emphasis on the fundamental theorems and their proofs. Prerequisite: MATH 311W.
486. MATHEMATICAL THEORY OF GAMES (3) Basic theorems, concepts, and methods in the
mathematical study of games of strategy; determination of optimal play when possible. Prerequisite:
MATH 484.
494. RESEARCH PROJECT (1 -12)
496. INDEPENDENT STUDIES (1 -18)
497. SPECIAL TOPICS (1 - 9)
498. SPECIAL TOPICS (1 - 9)
499. (GI) FOREIGN STUDIES (1 -12)
The University reserves the right to change the requirements and regulations listed here and to
determine whether a student has satisfactorily met its requirements for admission or graduation, and
to reject any applicant for any reason the University determines to be material to the applicant’s
G. Course Descriptions
45
qualifications to pursue higher education. Nothing in this material should be considered a guarantee
that completion of a program and graduation from the University will result in employment.
Review Date: 03/01/2002
Appendix H
Eligibility for
Membership in Phi Beta
Kappa
Phi Beta Kappa, the nation’s oldest and most distinguished national honor society recognizing
outstanding achievement in the liberal arts and sciences, was founded in 1776 at the College of
William and Mary in Williamsburg, Virginia. The Pennsylvania State University Chapter (Lambda
of Pennsylvania) was established in 1937.
Election to Phi Beta Kappa honors the quality and breadth of a student’s undergraduate academic
achievement. No formal application for Phi Beta Kappa membership is needed. The Chapter reviews
student records each spring to identify candidates.
The requirements for a student to be invited into membership in Phi Beta Kappa include:
(1) Candidates must have a non-professional major in the arts, humanities, social sciences, or
sciences. Most majors in the College of Liberal Arts, Eberly College of Science, College
of Earth and Mineral Sciences, and College of Arts and Architecture are acceptable. A
few majors in the College of Communications are also considered non-professional. Majors
in the College of Agricultural Sciences, Smeal College of Business Administration, College
of Education, College of Engineering, and College of Health and Human Development are
considered to be professional majors and are not accepted for Phi Beta Kappa membership.
(2) Candidates with 90 or more credits completed must have a 3.6 cumulative GPA. Candidates
with 60 to 89 credits completed must have a 3.8 GPA.
(3) Candidates must have completed a minimum of 60 credits at Penn State.
47
48
H. Eligibility for Membership in Phi Beta Kappa
(4) Candidates must have completed at least one foreign language course at the second level
(e.g., French 002, German 002, Japanese 002) OR must have equivalent credits granted
by Penn State through examination, transfer or advanced placement OR an official of
the student’s College (e.g. faculty adviser, department coordinator) must certify that the
student has the required foreign language competence. The latter option may be the case
when the student is a native speaker of another language.
(5) Candidates must have completed all of their Penn State General Education requirements
in the arts, humanities, social and behavioral sciences, natural sciences, and quantification.
(6) Candidates must have at least 80 percent of their total credits in liberal arts and science
courses OR at least 100 credits in total that are in liberal arts and science courses. Liberal
arts and science courses include most, although not all, of the courses from the approved
majors described above.
PHI BETA KAPPA
Lambda of Pennsylvania Chapter
The Pennsylvania State University
Dennis G. Shea, Ph.D.
114D Henderson Building
University Park, PA 16802
(814) 863-2900
FAX (814) 863-2905
E-mail: dgs4@psu.edu
www.personal.psu.edu/dgs4
http://www.personal.psu.edu/faculty/t/o/tob/pbk/