Handbook for Undergraduate Mathematics Majors Department of Mathematics and Statistics Penn State Altoona math.aa.psu.edu/degrees September 2008
.
Contents i
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 MT- SAL) 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) SUPPORTING LEVEL I: (4) COURSES (14 15) LEVEL II: (4) ( ) ( ) LEVEL III: (4) HUMANITIES (3 CR) ( ) OTHER CULTURES (3 CR): ( ) ( ) ( ) ( ) SOC./BEHAV. SCI ( ) (3 CR) ( ) ( ) ( ) Total Credits:
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) SOC./BEHAV.SCI (6CR) (GS) ENGL 202 (3) (GWS) ( ) ( ) CAS 100 (3) (GWS) ( ) ( ) NATURAL SCI. (9 CR) (GN) ( ) ( ) ( ) HUMANITIES (6 CR) (GH) HEALTH/PHYS. ACT. ( ) (3 CR) (GHA) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) US CULTURES (3 CR) (US) WRITING ACROSS THE FIRST-YEAR CURR. INT L CULTURES (3 CR) (IL) 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 & 6 CREDITS REPEATED COURSES 5 SENATE POLICY 83-80 Courses that do not meet Total Credits Earned: degree requirements: Source/Time for credit acquisition: (less repeats and remedial; 36 of the last 60 credits at PSU? must have at least 120) 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: Second Semester: Math 140 4 Math 141 4 Natural Science 3 Natural Science 3 Foreign Language I 4 Foreign Language II 4 Arts, Humanities or Soc. Sci. 3 English 15 3 First-Year Seminar 1 Health/Physical Activity 1.5 Total Semester Credits 15 Total Semester Credits 15.5 Third Semester: Fourth Semester: Math 220 2 Math 250 or 251 3 or 4 Math 230 4 Math 311W 3 Foreign Language III 4 CSE 121 or CMPSC 201C 3 Natural Science 3 CAS 100 3 Arts, Humanities or Soc. Sci. 3 Health/Physical Activity 1.5 Total Semester Credits 16 Total Semester Credits 13.5 14.5 Fifth Semester: Sixth Semester: Math 312 3 Math 403 3 Math 435 or Math 436 3 400-Level Math** 3 Supporting Course 3 or 4 Supporting Course 3 or 4 Other Cultures 3 English 202C 3 Arts, Humanities or Soc. Sci. 3 Arts, Humanities or Soc. Sci. 3 Total Semester Credits 15 16 Total Semester Credits 15 16 Seventh Semester: Eighth Semester: 400-Level Math* 3 400-Level Math** 3 Supporting Course 3 or 4 Supporting Course 3 or 4 Other Cultures 3 English 202C 3 Arts, Humanities or Soc. Sci. 3 Arts, Humanities or Soc. Sci. 3 Arts, Humanities or Soc. Sci. 3 Arts, Humanities or Soc. Sci. 3 Arts, Humanities or Soc. Sci. 3 Total Semester Credits 15 16 Total Semester Credits 12 13 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 311W* (3) MATH 141* (4) CMPSC 101 (3) OR MATH 250 (3) OR MATH 220 (2) CMPSC 201C (3) MATH 251 (4) 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 SUPPORTING MATH 414*(3) OR and 471. COURSES (15 16) 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) ( ) 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) SOC./BEHAV.SCI (6CR) (GS) ENGL 202 (3) (GWS) ( ) ( ) CAS 100 (3) (GWS) ( ) ( ) NATURAL SCI. (9 CR) (GN) ( ) ( ) ( ) HUMANITIES (6 CR) (GH) HEALTH/PHYS. ACT. ( ) (3 CR) (GHA) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) US CULTURES (3 CR) (US) WRITING ACROSS THE FIRST-YEAR CURR. INT L CULTURES (3 CR) (IL) 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 & 6 CREDITS REPEATED COURSES 5 SENATE POLICY 83-80 Courses that do not meet Total Credits Earned: degree requirements: Source/Time for credit acquisition: (less repeats and remedial; 36 of the last 60 credits at PSU? must have at least 120) 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: Second Semester: Math 140 4 Math 141 4 Natural Science 3 Natural Science 3 Foreign Language I 4 Foreign Language II 4 Arts, Humanities or Soc. Sci. 3 English 15 3 First-Year Seminar 1 Health/Physical Activity 1.5 Total Semester Credits 15 Total Semester Credits 15.5 Third Semester: Fourth Semester: Math 220 2 Math 250 or 251 3 or 4 Math 230 4 Math 311W 3 CAS 100 3 CSE 121 or CMPSC 201C 3 Natural Science 3 English 202C 3 Arts, Humanities or Soc. Sci. 3 Health/Physical Activity 1.5 Total Semester Credits 15 Total Semester Credits 13.5 14.5 Fifth Semester: Sixth Semester: Math 312 3 Math 403 3 Math 435 or Math 436 3 Math 414 3 Application Area Course 3 Application Area Course 3 Supporting Course 3 or 4 Supporting Course 3 or 4 Arts, Humanities or Soc. Sci. 3 Arts, Humanities or Soc. Sci. 3 Total Semester Credits 15 16 Total Semester Credits 15 16 Seventh Semester: Eighth Semester: 400-Level Math* 3 400-Level Math** 3 400-Level Math** 3 Application Area Course 3 Application Area Course 3 Supporting Course 3 or 4 Supporting Course 3 or 4 Arts, Humanities or Soc. Sci. 3 Arts, Humanities or Soc. Sci. 3 Total Semester Credits 15 16 Total Semester Credits 12 13 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 311W* (3) MATH 141* (4) CMPSC 101 (3) OR MATH 250 (3) OR MATH 220 (2) CMPSC 201C (3) MATH 251 (4) 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 SUPPORTING MATH 436*(3) and 471. COURSES (12 13) 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 ( ) ( ) ( ) 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) 19 3 GENERAL EDUCATION (40 credits) ENGL 15 OR 30 (3) (GWS) ARTS (6 CR) (GA) SOC./BEHAV.SCI (6CR) (GS) ENGL 202 (3) (GWS) ( ) ( ) CAS 100 (3) (GWS) ( ) ( ) NATURAL SCI. (9 CR) (GN) ( ) ( ) ( ) HUMANITIES (6 CR) (GH) HEALTH/PHYS. ACT. ( ) (3 CR) (GHA) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) US CULTURES (3 CR) (US) WRITING ACROSS THE FIRST-YEAR CURR. INT L CULTURES (3 CR) (IL) 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 & 6 CREDITS REPEATED COURSES 5 SENATE POLICY 83-80 Courses that do not meet Total Credits Earned: degree requirements: Source/Time for credit acquisition: (less repeats and remedial; 36 of the last 60 credits at PSU? must have at least 120) 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: Second Semester: Math 140 4 Math 141 4 Natural Science 3 Natural Science 3 Foreign Language I 4 Foreign Language II 4 Arts, Humanities or Soc. Sci. 3 English 15 3 First-Year Seminar 1 Health/Physical Activity 1.5 Total Semester Credits 15 Total Semester Credits 15.5 Third Semester: Fourth Semester: Math 220 2 Math 250 or 251 3 or 4 Math 230 4 Math 311W 3 CAS 100 3 CSE 121 or CMPSC 201C 3 Natural Science 3 English 202C 3 Arts, Humanities or Soc. Sci. 3 Health/Physical Activity 1.5 Total Semester Credits 15 Total Semester Credits 13.5 14.5 Fifth Semester: Sixth Semester: Math 312 3 300 or 400-Level Math* 3 Math 436 or Math 484 3 Math 414 3 Application Area Course 3 Application Area Course 3 Supporting Course 3 or 4 Supporting Course 3 or 4 Arts, Humanities or Soc. Sci. 3 Arts, Humanities or Soc. Sci. 3 Total Semester Credits 15 16 Total Semester Credits 15 16 Seventh Semester: Eighth Semester: Math 415 3 300 or 400-Level Math* 3 Math 484 or 436 3 400-Level Math** 3 Application Area Course 3 Application Area Course 3 Supporting Course 3 or 4 Arts, Humanities or Soc. Sci. 3 Arts, Humanities or Soc. Sci. 3 Total Semester Credits 15 16 Total Semester Credits 12 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.
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. Units of Study, Grades 9-12 Fewer than two Two or three Four or more Register in Course Level 001 (4 crs.) Course Level 002 (4 crs.) 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. probability but not statistics. An excellent course for mathematics majors interested in 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 R n, 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 R n to R m, 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 GEOM- ETRY (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.