Overview of proposals to limit double‐counting credits between  

A&S non‐interdisciplinary majors  

There are two relevant A&S rules:  A. 15‐credit rule for A&S minors  “Each minor must, however, include at least 15 credit hours that are being counted solely toward the minor.”  Vanderbilt Catalog, p. 72.  B. 6‐credit double‐counting limitation between an A&S interdisciplinary major and an A&S non‐interdisciplinary major  “Students may combine an interdisciplinary major with a major in one of the recognized fields listed at the beginning of this chapter. Upon approval of the Committee on Individual Programs and the student’s adviser, (a) as many as 6 hours may be counted as part of both the interdisciplinary major and the second major . . . “  Vanderbilt Catalog, p. 71.

Problem: How should the A&S faculty reasonably limit double‐counting credits between non‐interdisciplinary majors?  Motion tabled at December, 2010, A&S Faculty Meeting: Each major must include at least 24 credit hours that are being counted solely toward the A&S non‐interdisciplinary major  a.k.a. the CASP 24‐credit “floor” rule or the “strong” version or interpretation.  A&S, at present, has no rule regarding the number of credits that a student may double‐count between two A&S non‐interdisciplinary majors, which means that there is no limit to double‐counting credits between two such majors.    Why is a rule advisable?       

From the A&S Registrar, Molly Thompson: Here are the possibly problematic combinations:  ASTD/HART: 9 hours HART may count toward ASTD CCIV/HART: 9 hours HART may count toward CCIV CCIV/PHIL: 6 hours PHIL may count toward CCIV CMST/ENGL‐W: 6 hours ENGL may count toward CMST CMST/PHIL: 9 hours PHIL may count toward CMST CMST/SOC: 9 hours SOC may count toward CMST CMST/PSCI: 6 hours PSCI may count toward CMST CMST/PSY: 6 hours PSY may count toward CMST GER /xx: German Studies major requires 6 hours in “German text” and 6 hours in “German content,” none of which are defined.  That is possibly 6 to up to 12 hours of double‐counting action. HIST/CLAS: 21 hours CLAS may count toward HIST HIST/ECON: 12 hours ECON may count toward HIST HIST/RLST: 6 hours RLST may count toward HIST MATH‐2/xx: 6 hours outside the department  (For MATH/ECON, as you may know, a student could double‐count 9 hours.) PSY‐R/xx: 6 hours BME, CS, EECE, MATH, PHIL, ANTH, BSCI, SOC may count toward PSY major RLST/CLAS: 9 hours CLAS may count toward RLST RLST/HIST: 21 hours HIST may count toward RLST RLST/PHIL: 12 hours PHIL may count toward RLST 

Goals of such a rule limiting double counting credits between A&S non‐interdisciplinary majors:  1. Set reasonable limit on double‐counting.  2. Ensure that students take a unique set of courses to fulfill major.  3. Protect integrity of major.  4. Prevent it from being more difficult to earn a minor than a second major. 

First attempt at a rule (April‐May 2010):  

Extend the 6‐credit limitation between an interdisciplinary major and a non‐interdisciplinary major to two A&S non‐interdisciplinary majors.  Approved by CASP and FC, not approved by the A&S faculty. 

30 30 36 36 42 42 48 48 48 30Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2

101 101 101 101 101 101 101 101 101 101102 102 102 102 102 102 102 102 102 102

1 103 111 1 103 113 103 115 103 117 1032 104 112 2 104 114 104 116 104 118 1043 105 113 3 1 105 115 1 105 117 105 119 1054 106 114 4 2 106 116 2 106 118 106 120 1065 107 115 5 3 107 117 3 1 107 119 1 107 121 1076 108 116 6 4 108 118 4 2 108 120 2 108 122 1087 109 117 7 5 109 119 5 3 109 121 3 1 109 123 1 1 109 117 18 110 118 8 6 110 120 6 4 110 122 4 2 110 124 2 2 110 118 2

7 111 121 7 5 111 123 5 3 111 125 3 3 111 119 38 112 122 8 6 112 124 6 4 112 126 4 4 112 120 4

7 113 125 7 5 113 127 5 5 113 121 58 114 126 8 6 114 128 6 6 114 122 6

7 115 129 7 7 115 123 78 116 130 8 8 116 124 8

Student Must Complete:

6 hour Maximum overlap ruleSteady overlap, progressive increase in unique hours. All courses = 3 credits. Courses in gold double‐count.

54hrs of 60 66hrs of 72 78hrs of 84 90hrs of 96 72hrs of 78

Second attempt at a rule (November‐December, 2010):  

CASP has proposed, using the 15‐credit rule for minors as a model, a 24‐credit “floor” for each A&S non‐interdisciplinary major.  “Each major must include at least 24 credit hours that are being counted solely toward the A&S non‐interdisciplinary major.  It should be noted that adoption of this rule would apply also to the non‐interdisciplinary major for those students who combine such a major with an interdisciplinary major."  This is the "strong" interpretation or version of the 24‐credit minimum requirement. 

Approved by CASP and FC, tabled at December A&S Faculty Meeting. 

30 30 36 36 42 42 48 48 48 30Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2

101 101 101 101 101 101 101 101 101102 102 102 102 102 102 102 102 102

1 103 111 1 103 103 103 103 103 103 1032 104 112 2 104 104 104 104 104 104 1043 105 113 3 1 105 113 1 105 105 105 105 1054 106 114 4 2 106 114 2 106 106 106 106 1065 107 115 5 3 107 115 3 1 107 115 1 107 107 107 1076 108 116 6 4 108 116 4 2 108 116 2 108 108 108 1087 109 117 7 5 109 117 5 3 109 117 3 1 109 117 1 1 109 117 18 110 118 8 6 110 118 6 4 110 118 4 2 110 118 2 2 110 118 2

7 111 119 7 5 111 119 5 3 111 119 3 3 111 119 38 112 120 8 6 112 120 6 4 112 120 4 4 112 120 4

7 113 121 7 5 113 121 5 5 113 121 58 114 122 8 6 114 122 6 6 114 122 6

7 115 123 7 7 115 123 78 116 124 8 8 116 124 8

103 111 105 113 107 115 109 117 109 117104 112 106 114 108 116 110 118 110 118105 113 107 115 109 117 111 119 111 119106 114 108 116 110 118 112 120 112 120107 115 109 117 111 119 113 121 113 121108 116 110 118 112 120 114 122 114 122109 117 111 119 113 121 115 123 115 123110 118 112 120 114 122 116 124 116 124

24 hours counted in each major that are not counted in the other major AT ALL

72hrs of 7872hrs of 9660hrs of 72 66hrs of 8454hrs of 60Student Must Complete:

Steady unique hours with progressive increase in overlap. All courses = 3 credits. Courses in gold double‐count.Strong Interpretation of the 24 hour standard minimum hours

Revised version of the 24‐credit minimum rule, as proposed by Professors David Cliffel and John Rafter after the December A&S Faculty Meeting:   “Each major must include a minimum of 24 credit hours that are not being counted as part of the 24 credit hour minimum toward another major.”  This is the "weak" interpretation or version of the 24‐credit minimum requirement. 

30 30 36 36 42 42 48 48 48 30Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2

101 101 1 101 101 1 101 101 1 101 101 1 101 101 1102 102 2 102 102 2 102 102 2 102 102 2 102 102 2

1 103 111 3 103 103 3 103 103 3 103 103 3 103 103 32 104 112 4 104 104 4 104 104 4 104 104 4 104 104 43 105 113 5 1 105 113 5 105 105 5 105 105 5 105 105 54 106 114 6 2 106 114 6 106 106 6 106 106 6 106 106 65 107 115 7 3 107 115 7 1 107 115 7 107 107 7 107 107 76 108 116 8 4 108 116 8 2 108 116 8 108 108 8 108 108 87 109 109 5 109 109 3 109 109 1 109 109 1 109 1098 110 110 6 110 110 4 110 110 2 110 110 2 110 110

7 111 111 5 111 111 3 111 111 3 1118 112 112 6 112 112 4 112 112 4 112

7 113 113 5 113 113 5 1138 114 114 6 114 114 6 114

7 115 115 7 1158 116 116 8 116

1 103 101 105 101 107 101 109 101 109 1012 104 102 106 102 108 102 110 102 110 1023 105 111 107 103 109 103 111 103 111 1034 106 112 108 104 110 104 112 104 112 1045 107 113 109 113 111 105 113 105 113 1056 108 114 110 114 112 106 114 106 114 1067 109 115 111 115 113 115 115 107 115 1078 110 116 112 116 114 116 116 108 116 108

Student Must only complete:48hrs of 60 48 hrs of 72 48hrs of 84

Progressive reduction in unique courses and increase in overlap. All courses = 3 credits.  Courses in gold double‐count.

24 hours counted in each major that are not counted in the other major's 24 hours

Weak Interpretation of the 24 hour standard minimum hours ‐ 48 hours needed to satisfy any major combination

48hrs of 96 48hrs of 78

Revised or alternative version of the 24‐credit minimum rule as proposed by Professors Gieri Simonett and John Rafter on March 1, 2011:   “Each major must include a minimum of 27 credit hours that are not being counted as part of the 27 credit hour minimum toward another major.”  This is version 2 of the "weak" interpretation, with a 27‐credit minimum requirement. 

30 30 36 36 42 42 48 48 48 30Major 1 Major 2 Major 1Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2

101 101 1 101 101 1 101 101 1 101 101 1 101 101 11 118 102 2 102 102 2 102 102 2 102 102 2 102 102 22 103 111 3 103 103 3 103 103 3 103 103 3 103 103 33 104 112 4 1 118 104 4 104 104 4 104 104 4 104 104 44 105 113 5 2 105 113 5 105 105 5 105 105 5 105 105 55 106 114 6 3 106 114 6 1 118 106 6 106 106 6 106 106 66 107 115 7 4 107 115 7 2 107 115 7 107 107 7 107 107 77 108 116 8 5 108 116 8 3 108 116 8 1 117 108 8 1 117 108 88 109 117 9 6 109 117 9 4 109 117 9 2 109 118 9 2 118 109 99 110 110 7 110 110 5 110 110 3 110 110 3 110 110

8 111 111 6 111 111 4 111 111 4 1119 112 112 7 112 112 5 112 112 5 112

8 113 113 6 113 113 6 1139 114 114 7 114 114 7 114

8 115 115 8 1159 116 116 9 116

1 103 101 105 101 107 101 109 101 117 1012 104 102 106 102 108 102 110 102 110 1023 105 111 107 103 109 103 111 103 111 1034 106 112 108 104 110 104 112 104 112 1045 107 113 109 113 111 105 113 105 113 1056 108 114 110 114 112 106 114 106 114 1067 109 115 111 115 113 115 115 107 115 1078 110 116 112 116 114 116 116 108 116 1089 118 117 118 117 118 117 117 118 118 109

27 hours counted in each major that are not counted in the other major's 27 hours

Weak interpretation version 2 of the 24 hour standard minimum hours. All courses=3 credits. Gold = double‐count.

54hrs of 96 54hrs of 78Student Must only complete:

54hrs of 60 54 hrs of 72 54hrs of 84

How do the three versions satisfy the goals? 

 

6‐credit double‐counting limit 

Strong version 

Weak versions 

Reasonable limit on double‐counting  yes  some  no 

Unique set of courses  some  yes  no 

Integrity of major  some  yes  no 

Minor harder than second major  no  no  yes 

    

Three concerns have been expressed about the “strong” interpretation:  One objection that has been raised against the strong version is that it would "seriously limit double majoring."  Yet, according to the A&S Registrar, Molly Thompson, only one of the most popular double‐major combinations would be affected by the strong version (ECON/MATH).    In the five‐year period from 06F‐11S, our most popular double‐major combinations on average were as follows:  ECON/PSCI ECON/ES (Engineering Science) H&OD/SPAN HIST/PSCI ECON/SPAN ECON/H&OD ECON/MATH PSCI/SPAN PHIL/PSCI MHS/SPAN MATH/PHYS PSY/SPAN MHS/PSY ECON/ENGL ECON/PHIL ENGL/PSCI CMST/SPAN MCB/SPAN PSY/SOC ENGL/PSY 

ENGL/SPAN ENGL/HIST  Each of the majors listed above requires at least 30 hours.  With three exceptions, the non‐interdisciplinary double‐major combinations do not have any courses that can be double‐counted.  The three exceptions are the ECON/MATH combination (which causes problems only with the Econ/Math subprogram II combination, a combination that has been declared once since the introduction of subprogram II); the MATH/PHYS combination (in which six hours of PHYS credit can count toward the MATH II major, but no MATH credits may count toward Physics); and the PSY/SOC combination (in which six hours of SOC credit can count toward the PSY‐R and PSY‐H majors, but no PSY credits may count toward Sociology).  Therefore, with all of these double‐majors except ECON/MATH II, students have had no problems—nor could they have any problems—completing at least 24 hours specific toward each major.  As we have already shown, the one student who had the ECON/MATH II combination did not have a problem completing 24 hours specific toward each of those majors, either. 

         

A second concern, from the Mathematics department, is that at present students are able to earn a double major in Economics and Mathematics by taking 30 credits in Economics and 29 credits in Mathematics, but, if the CASP recommendation were to be approved, this would no longer be possible. 

This is true under some very limited circumstances (6 conditions would have to be met simultaneously) and, even then, the Economics/Mathematics program 2 double major would fall just one Mathematics credit short.  The 6 conditions: Student chooses Math program II; and satisfies ECON statistics requirement with MATH 218 and 219; and did not take ECON 150 or MATH 218L; and has exactly 29 MATH credits; and has taken no additional MATH or ECON courses at all; and uses ECON to satisfy MATH‐Program 2 non‐MATH courses. 

It is very unlikely, according to the A&S Registrar’s Office, that all 6 conditions would be met at the same time.   MATH-2 Hrs ECON Hrs Required 35 Required 33

MATH 155a 4 ECON 100 3

MATH 155b 4 ECON 101 3

MATH 175 3 MATH 218 3

MATH 204 3 ECON 226 3

MATH 208 3 ECON 231 3

MATH 218 3 ECON 232 3

MATH 219 3 ECON 235 3

MATH 246a 3 ECON 253 3

MATH 246b 3 ECON 263 3

ECON 253 3 ECON 273 3

ECON 273 3 ECON 274 3

Total 35 Total 33MATH 219 is required in ECON, but does not count in the ECON total hours, for it is one of the alternatives to the ECON 150 option. Hence, only 3 hours of MATH 218 and 219 count in the ECON major, since they are, together, taken instead of ECON 150.

35 – 12 = 23 33 – 9 = 24

    

A student would fulfill the requirements for an Economics/Mathematics double major under both weak versions without any additional coursework.  MATH-Program 2 Hrs ECON Hrs

Required 35 Required 33

MATH 155a 4 ECON 100 3 1

MATH 155b 4 ECON 101 3 2

MATH 175 3 ECON 226 3 3

MATH 204 3 8 ECON 231 3 4

MATH 208 3 7 ECON 232 3 5

MATH 219 3 6 ECON 235 3 6

MATH 246a 3 5 ECON 263 3 7

MATH 246b 3 4 ECON 274 3 8

ECON 253 3 3 ECON 253 3

ECON 273 3 2 ECON 273 3

MATH 218 3 1 MATH 218 3

Total 35 Total 33 Satisfies weak version √ √

MATH-Program 2 Hrs ECON Hrs

Required 35 Required 33

MATH 155a 4 ECON 100 3 1

MATH 155b 4 9 ECON 101 3 2

MATH 175 3 8 ECON 226 3 3

MATH 204 3 7 ECON 231 3 4

MATH 208 3 6 ECON 232 3 5

MATH 219 3 5 ECON 235 3 6

MATH 246a 3 4 ECON 263 3 7

MATH 246b 3 3 ECON 274 3 8

ECON 253 3 ECON 253 3 9

ECON 273 3 2 ECON 273 3

MATH 218 3 1 MATH 218 3

Total 35 Total 33

Satisfies weak version 2 √ √

     

In response to this concern, Dean Dever, in consultation with Faculty Council and with the A&S Parliamentarian, has added a note of clarification to the motion: 

 The A&S faculty encourages students to petition the Administrative Committee if s/he is double‐majoring in Economics and Mathematics and finds herself/himself one credit short of fulfilling both majors because of the 24‐credit “floor” rule.  The A&S Registrar shall keep a record of the number of petitions received and granted by the Administrative Committee that are related to this rule.    

A third concern, from the Mathematics department, is that another A&S department or program might add Mathematics courses to its list of required courses that count toward the major, thereby making it more difficult to double major in that discipline and Mathematics. 

         

MATH-Program 2 Hrs * CHEM Hrs

*

Required 35 Required 40

MATH 155a 4 CHEM 102a-b 0

MATH 155b 4 CHEM 104a-b 0

MATH 175 3 3 CHEM 219a-b 2 2 MATH 204 3 6 CHEM 220a-b 6 8

MATH 208 3 9 CHEM 210/212a 4 12

MATH 219 3 12 CHEM 230 3 15 MATH 246a 3 15 CHEM 236 1 16 MATH 246b 3 18 BSCI 220 3 19 CHEM 2xx 3 CHEM 203 3 22 CHEM 2xx 3 CHEM 2xx/2xx 6

MATH 218 3 21 CHEM 295a-b 4 26

MATH 155a-b 8 * = cumulative unique credit hours

9797

A&S

College of Arts and Science / Chemistry

John A. McLean, Jens MeilerRESEARCH ASSISTANT PROFESSORS Anthony P. Gies, Hye-Young

Kim, Kwangho Kim, Ashwath Jayagopal, Dmitry Koktysh, Ivan Kozekov, James R. McBride, Ganesh Shanmugam, Donald F. Stec, Keri A. Tallman, Ian D. Tomlinson, Markus W. Voehler, Alex G. Waterson, Huiyong Yin

ADJOINT ASSISTANT PROFESSOR Andrienne C. FriedliSENIOR LECTURERS Adam K. List, Shawn T. Phillips, Michelle M.

Sulikowski, Grace ZoorobLECTURER Tara D. Todd

THE Department of Chemistry seeks to provide a sound education in the fundamentals of modern chemistry as well as exposure to cutting-edge research and contemporary instru-mentation in the field. This is accomplished by providing students with a solid background in the disciplines of organic, analytical, inorganic, biological, and physical chemistry. The core courses in these areas, which are supported by a variety of practical experimental experiences in the laboratory, pro-vide students with the skills needed to think critically about chemistry. After these core courses, students delve deeper into an area of their choice. Recognizing the importance of research, which integrates and makes sense of our collective body of knowledge, we encourage students to participate in undergraduate research. The chemistry major at Vanderbilt University meets the guidelines for the American Chemical Society approved program of study in chemistry.

Program of Concentration in ChemistryThe chemistry program is organized into four parts. The first part is a general chemistry course sequence (Chem 102a–102b and 104a–104b or AP credit) to serve as an entry point into the major. The second part consists of foundation courses in the five major disciplines of chemistry: analytical (210), bio-chemistry (BSCI 220), inorganic (203), organic (220a–220b or 218a–218b), and physical (230 or 231). The third part of the chemistry major consists of completing 8 credit hours of laboratory past 104a–104b. Four hours are from laboratory courses (219a–219b, 212a, and 236) associated with foundation courses. There are also 4 credit hours of a capstone laboratory (295a–295b) designed to provide advanced laboratory experi-ence. The fourth part of the major consists of completing a min-imum of 6 credit hours of in-depth chemistry courses. These in-depth courses build upon the content of foundation courses or integrate concepts from these foundational disciplines.

Concentration in ChemistryRequired Non-chemistry Courses

One year of calculus (MATH 155a–155b is preferred) PHYS: Both 116a–116b and 118a–118b or 121a–121bRequired Chemistry Courses Hours toward major

Chem 102a–102b & 104a–104b or AP credit 0 Chem 220a–220b (or 218a–218b) & 219a–219b 8 Chem 210 & 212a 4 Chem 230 or 231 3 Chem 236 1 BSCI 220 3 Chem 203 3 *Two in-depth chemistry courses 6 Chem 295a–295b 4 Minimum Hours for Chemistry Major 32

* In-depth chemistry courses include all 200-level chemistry

courses not explicitly required, except for Chem 250 and 292a–292b–292c. Other in-depth chemistry courses are Chemical and Biomolecular Engineering 223 and 225, and Earth and Environmental Sciences 260, and any 300-level chemistry lecture courses. (Qualified seniors interested in 300-level courses must obtain approval from the course instructor, their adviser, and the director of graduate studies in chemistry. Further details are found in the Academic Policies for the College of Arts and Science.) A maximum of 3 credit hours of chemistry research (282) may be counted as in-depth chemis-try course hours.

Additional math courses, such as Math 175 and Math 218, are highly recommended for the chemistry major.

Options for Concentration in ChemistryIn-depth chemistry courses can be chosen so as to define a focus area within chemistry. Students should consult with their major adviser about focus area options, or to formulate an individualized focus area option. Further descriptions of these options and other recommended courses can be found in the chemistry major handbook on the chemistry depart-ment homepage.

Chemical Biology Focus. The role of chemical processes in biological systems is fundamental to chemical biology. The journal Nature Chemical Biology defines chemical biology as

“the use of chemistry to advance a molecular understanding of biology and the harnessing of biology to advance chemistry.” Biological chemistry builds upon the disciplines of medicinal chemistry, biochemistry, pharmacology, genetics, bioorganic and organic chemistry. Suggested in-depth chemistry electives: 202, 220c, 224, 226, 282.

Chemical Sciences Focus. This option provides a broad foundation of chemistry, permitting the greatest flexibility in future career pathways and providing an excellent preparation for positions in chemical industry and for graduate programs in chemistry. Suggested in-depth chemistry electives: 211, 230, 231, 282.

Environmental Chemistry Focus. Environmental chemis-try concerns the chemical phenomena that occur in nature. Environmental chemistry spans atmospheric, aquatic, and soil chemistry with a reliance on analytical chemistry for methods of analysis. Environmental chemistry can be applied to the under-standing of issues such as ground water pollution, wastewater treatment, ozone depletion, and greenhouse gas emissions. Sug-gested in-depth chemistry electives: 211, 230, 231, 282, EES 260.

Materials Chemistry Focus. Materials chemistry is concerned with designing and synthesizing new materials with specific useful properties and determining the relationships between physical properties and the composition and structure of these new materials. Materials chemistry encompasses all size regimes from bulk to nanoscale. Synthetic chemistry (inorganic and organic), physical chemistry, and analytical chemistry are all important components of this field. Suggested in-depth chemis-try electives: 211, 222, 230, 231, 235, 240, 282, 338, 350.

Minor in ChemistryThe minor in chemistry requires 18 hours of course work, including 4 hours from 102b and 104b or AP credit, and 14 hours selected from any of the courses acceptable for the major in chemistry.

In response to this concern, Dean Dever, in consultation with Faculty Council and with the A&S Parliamentarian, has added a second note of clarification to the motion: 

The Committee on Educational Programs (CEP) shall carefully review the impact of proposed program revisions on popular double‐major combinations, especially with regards to the 24‐credit “floor” rule. 

30 30 36 36 42 42 48 48 48 30Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2

101 101 101 101 101 101 101 101 101 101102 102 102 102 102 102 102 102 102 102

1 103 111 1 103 113 103 115 103 117 1032 104 112 2 104 114 104 116 104 118 1043 105 113 3 1 105 115 1 105 117 105 119 1054 106 114 4 2 106 116 2 106 118 106 120 1065 107 115 5 3 107 117 3 1 107 119 1 107 121 1076 108 116 6 4 108 118 4 2 108 120 2 108 122 1087 109 117 7 5 109 119 5 3 109 121 3 1 109 123 1 1 109 117 18 110 118 8 6 110 120 6 4 110 122 4 2 110 124 2 2 110 118 2

7 111 121 7 5 111 123 5 3 111 125 3 3 111 119 38 112 122 8 6 112 124 6 4 112 126 4 4 112 120 4

7 113 125 7 5 113 127 5 5 113 121 58 114 126 8 6 114 128 6 6 114 122 6

7 115 129 7 7 115 123 78 116 130 8 8 116 124 8

Student Must Complete:

6 hour Maximum overlap ruleSteady overlap, progressive increase in unique hours. All courses = 3 credits. Courses in gold double‐count.

54hrs of 60 66hrs of 72 78hrs of 84 90hrs of 96 72hrs of 78

30 30 36 36 42 42 48 48 48 30Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2

101 101 101 101 101 101 101 101 101102 102 102 102 102 102 102 102 102

1 103 111 1 103 103 103 103 103 103 1032 104 112 2 104 104 104 104 104 104 1043 105 113 3 1 105 113 1 105 105 105 105 1054 106 114 4 2 106 114 2 106 106 106 106 1065 107 115 5 3 107 115 3 1 107 115 1 107 107 107 1076 108 116 6 4 108 116 4 2 108 116 2 108 108 108 1087 109 117 7 5 109 117 5 3 109 117 3 1 109 117 1 1 109 117 18 110 118 8 6 110 118 6 4 110 118 4 2 110 118 2 2 110 118 2

7 111 119 7 5 111 119 5 3 111 119 3 3 111 119 38 112 120 8 6 112 120 6 4 112 120 4 4 112 120 4

7 113 121 7 5 113 121 5 5 113 121 58 114 122 8 6 114 122 6 6 114 122 6

7 115 123 7 7 115 123 78 116 124 8 8 116 124 8

103 111 105 113 107 115 109 117 109 117104 112 106 114 108 116 110 118 110 118105 113 107 115 109 117 111 119 111 119106 114 108 116 110 118 112 120 112 120107 115 109 117 111 119 113 121 113 121108 116 110 118 112 120 114 122 114 122109 117 111 119 113 121 115 123 115 123110 118 112 120 114 122 116 124 116 124

24 hours counted in each major that are not counted in the other major AT ALL

72hrs of 7872hrs of 9660hrs of 72 66hrs of 8454hrs of 60Student Must Complete:

Steady unique hours with progressive increase in overlap. All courses = 3 credits. Courses in gold double‐count.Strong Interpretation of the 24 hour standard minimum hours

30 30 36 36 42 42 48 48 48 30Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2

101 101 1 101 101 1 101 101 1 101 101 1 101 101 1102 102 2 102 102 2 102 102 2 102 102 2 102 102 2

1 103 111 3 103 103 3 103 103 3 103 103 3 103 103 32 104 112 4 104 104 4 104 104 4 104 104 4 104 104 43 105 113 5 1 105 113 5 105 105 5 105 105 5 105 105 54 106 114 6 2 106 114 6 106 106 6 106 106 6 106 106 65 107 115 7 3 107 115 7 1 107 115 7 107 107 7 107 107 76 108 116 8 4 108 116 8 2 108 116 8 108 108 8 108 108 87 109 109 5 109 109 3 109 109 1 109 109 1 109 1098 110 110 6 110 110 4 110 110 2 110 110 2 110 110

7 111 111 5 111 111 3 111 111 3 1118 112 112 6 112 112 4 112 112 4 112

7 113 113 5 113 113 5 1138 114 114 6 114 114 6 114

7 115 115 7 1158 116 116 8 116

1 103 101 105 101 107 101 109 101 109 1012 104 102 106 102 108 102 110 102 110 1023 105 111 107 103 109 103 111 103 111 1034 106 112 108 104 110 104 112 104 112 1045 107 113 109 113 111 105 113 105 113 1056 108 114 110 114 112 106 114 106 114 1067 109 115 111 115 113 115 115 107 115 1078 110 116 112 116 114 116 116 108 116 108

Student Must only complete:48hrs of 60 48 hrs of 72 48hrs of 84

Progressive reduction in unique courses and increase in overlap. All courses = 3 credits.  Courses in gold double‐count.

24 hours counted in each major that are not counted in the other major's 24 hours

Weak Interpretation of the 24 hour standard minimum hours ‐ 48 hours needed to satisfy any major combination

48hrs of 96 48hrs of 78

30 30 36 36 42 42 48 48 48 30Major 1 Major 2 Major 1Major 2 Major 1 Major 2 Major 1 Major 2 Major 1 Major 2

101 101 1 101 101 1 101 101 1 101 101 1 101 101 11 118 102 2 102 102 2 102 102 2 102 102 2 102 102 22 103 111 3 103 103 3 103 103 3 103 103 3 103 103 33 104 112 4 1 118 104 4 104 104 4 104 104 4 104 104 44 105 113 5 2 105 113 5 105 105 5 105 105 5 105 105 55 106 114 6 3 106 114 6 1 118 106 6 106 106 6 106 106 66 107 115 7 4 107 115 7 2 107 115 7 107 107 7 107 107 77 108 116 8 5 108 116 8 3 108 116 8 1 117 108 8 1 117 108 88 109 117 9 6 109 117 9 4 109 117 9 2 109 118 9 2 118 109 99 110 110 7 110 110 5 110 110 3 110 110 3 110 110

8 111 111 6 111 111 4 111 111 4 1119 112 112 7 112 112 5 112 112 5 112

8 113 113 6 113 113 6 1139 114 114 7 114 114 7 114

8 115 115 8 1159 116 116 9 116

1 103 101 105 101 107 101 109 101 117 1012 104 102 106 102 108 102 110 102 110 1023 105 111 107 103 109 103 111 103 111 1034 106 112 108 104 110 104 112 104 112 1045 107 113 109 113 111 105 113 105 113 1056 108 114 110 114 112 106 114 106 114 1067 109 115 111 115 113 115 115 107 115 1078 110 116 112 116 114 116 116 108 116 1089 118 117 118 117 118 117 117 118 118 109

27 hours counted in each major that are not counted in the other major's 27 hours

Weak interpretation version 2 of the 24 hour standard minimum hours. All courses=3 credits. Gold = double‐count.

54hrs of 96 54hrs of 78Student Must only complete:

54hrs of 60 54 hrs of 72 54hrs of 84