CANs List

Curriculum Action Notice


From:

Academic Affairs Committee

Date:

September 21, 2006

This is a bulletin from the Academic Affairs Committee concerning proposed curricular actions. Please forward any comments or concerns in the next 10 days to the AAC chair, Teri Doerksen, G04C Belknap Hall, ext. 4588.

CURRICULAR ACTION NOTICE: MATHEMATICS AND CIS

1. Program Change Proposal – BSE Mathematics

Rationale for change:

We are dropping the American History requirement, because PDE no longer requires BSE programs to have it, and we believe that other general education choices are equally valid. We are also adding complementary versions of some of our core upper-level math courses. In the past, for example, we have offered one semester of MA 3361-Modern Algebra each Spring. We propose an offering of two Modern Algebra courses, one focusing on the study of groups and one focusing on rings, in alternating Spring semesters. We have come to the realization that a study of groups alone, and of rings alone, meets the needs of secondary teachers and the standards of PDE, NCATE, and NCTM. This also allows us to better serve those students planning graduate study in mathematics (a full year of Algebra is standard preparation), and it also gives all of our math students an extra course to use as an elective. A limited supply of upper-level math electives is the most serious concern for our math programs (we have known this for some time, and this was also pointed out by our program review external reviewer). We propose that either Modern Algebra course, MA 3361 or MA 3362, will meet program requirements, and that both courses can be taken for credit in no particular order. In this first round of de-sequencing, we are proposing similar plans for MA 3329/3330-Modern Geometry, MA 3305/3306-History of Mathematics.

List all changes:

Remove requirement of HST 2201 OR HST 2202.

Replace requirement of MA 3304 – History and Philosophy of Mathematics with

  • MA 3304(History and Philosophy of Mathematics)
  • OR MA 3305(History of Mathematics from Counting to Calculus)
  • OR MA 3306(History of Mathematics from Calculus to Computers)

Replace requirement of MA 3329(Modern Geometry I) with

  • MA 3329(Uniform Geometries)
  • OR MA 3330(Non-uniform Geometries)

Replace requirement of MA 3361(Modern Algebra I) with

  • MA 3361(Modern Algebra – Groups)
  • OR MA 3362(Modern Algebra – Rings)
Impact on other programs (if any): Programs that require upper-level mathematics courses may expand choices for specific requirements, and students in those programs will have more choices for elective courses. None of the math courses involved are specific requirements of non-math programs. Dropping the history requirement will cause a small shift of enrollment to other Humanities Block courses (0 to 10 students per year).

2. Program Change Proposal – BS Mathematics – Pure Mathematics Concentration Rationale for change: The department is de-sequencing pairs of math courses required in the BSE Mathematics program. Of these, MA 3361- Modern Algebra I is a required course in the BS Mathematics - Pure Math program, and we are proposing here a change similar to those being made in the BSE program. In particular, either of the new courses MA 3361 and MA 3362 may be used to meet the Modern Algebra requirement. Those students planning to attend graduate school in mathematics will be advised to take both courses. List all changes: Replace requirement of MA 3361(Modern Algebra I) with
  • MA 3361(Modern Algebra – Groups)
  • OR MA 3362 (Modern Algebra – Rings)
3. Course Change Request – MA 3361 Purpose and nature of change: We propose reordering the topics in the existing courses MA 3361 and MA 3362 so that the courses can be taken independently. In particular, each course will meet PDE, NCATE, and NCTM program standards on their own, and can be taken together to meet graduate school expectations. Neither course will be a prerequisite for the other and both may be taken for credit. Old Course Title: Modern Algebra I New Course Title: Modern Algebra – Groups Course Description for Catalog (limit to four sentences): A study of abstract algebraic structures focusing on groups. Topics include: dihedral groups, cyclic groups, permutation groups, subgroups, cosets, quotient groups, homomorphisms, isomorphisms, cardinality, generators and relations, Lagrange’s theorem, Cayley’s theorem, the fundamental homomorphism theorem, the fundamental theorem for abelian groups, and applications of groups. MA 3361 and MA 3362 may both be taken for credit, and either course can be taken before the other.
Prerequisites: MA 3260 – Discrete Structures or permission of instructor.
Describe any student enrollment restrictions (limited to majors in program XXX, restricted from majors in program XXX, etc.): The new courses are less restrictive than the old. MA 3362 may be taken before MA 3361, and either may be taken to satisfy program requirements.

4. Course Change Request – MA 3362 Purpose and nature of change: We propose reordering the topics in the existing courses MA 3361 and MA 3362 so that the courses can be taken independently. In particular, each course will meet PDE, NCATE, and NCTM program standards on their own, and can be taken together to meet graduate school expectations. Neither course will be a prerequisite for the other and both may be taken for credit. Old Course Title: Modern Algebra II New Course Title: Modern Algebra - Rings Course Description for Catalog (limit to four sentences): A study of abstract algebraic structures focusing on rings. Topics include: rings, integral domains, fields, subrings, ideals, quotient rings, fields of quotients, the division algorithm, factorization of polynomials (reducibility and unique factorization), field extensions, and applications of rings/fields. MA 3361 and MA 3362 may both be taken for credit, and either course can be taken before the other.
Prerequisites: (Courses which MUST be completed prior to taking this course) MA 3260 – Discrete Structures or permission of instructor.
Describe any student enrollment restrictions (limited to majors in program XXX, restricted from majors in program XXX, etc.) The new courses are less restrictive than the old. MA 3362 may be taken before MA 3361, and either may be taken to satisfy program requirements.


5. New Course Request – MA 3305 History of Mathematics from Counting to Calculus

Purpose and Nature of Course: This is one of two new courses being developed to take the place of MA 3304 History and Philosophy of Mathematics. The two courses will be independent of each other with only a small overlap in material (essentially one chapter). They may be taken in either order, and either one will satisfy the PDE, NCATE, and NCTM standards. Both may be taken for credit. Course Description for Catalog (limit to four sentences): An in-depth study of the chronological development of facets of mathematics up to the development of Calculus. The historical background of each facet is integrated with experience in mathematical study and application. Emphasis is placed on great mathematicians, their contributions, and their methods of reasoning, including the contributions of underrepresented groups and diverse cultures. Concepts of number, number systems, and the nature of axiomatic reasoning are also covered. Co-requisite: MA 3260 Describe any student enrollment restrictions (limited to majors in program XXX, restricted from majors in program XXX, etc.) None – this course or MA 3306 will be required for all BSE majors and may be taken as an upper –division elective for any Mathematics program. The course will be open to anyone with the co-requisite.


6. Course Change Request – MA 3329
Purpose and nature of change: We propose re-sequencing the topics in the existing courses MA 3329 and MA 3330 so that the courses can be taken independently. In particular, each course will meet PDE, NCATE, and NCTM program standards on their own, and can be taken together to meet graduate school expectations. MA 3329 will be a traditional one-semester Modern Geometry course with emphasis on the axiomatic approach of Euclid and Hilbert, and MA 3330 will take a more contemporary track with emphasis on the analytic approach of Descartes, Gauss, and Riemann. Neither course will be a prerequisite for the other and both may be taken for credit. Old Course Title: Modern Geometry I New Course Title: Uniform Geometries Course Description for Catalog (limit to four sentences): A study of the traditional modern geometries. Topics include: Euclid’s postulate system with special focus on his Fifth Postulate, Hilbert’s axiom system, the hyperbolic axiom system, spherical geometry, the Gauss-Bonnet theorem for triangles, and Klein’s transformational geometry. MA 3329 and MA 3330 may both be taken for credit, and either course can be taken before the other.
Prerequisites: (Courses which MUST be completed prior to taking this course) MA 3260 – Discrete Structures or permission of instructor.
Describe any student enrollment restrictions (limited to majors in program XXX, restricted from majors in program XXX, etc.) The new courses are less restrictive than the old. MA 3329 may be taken before MA 3330, and either may be taken to satisfy program requirements.


7. Course Change Request – MA 3330
Purpose and nature of change: We propose re-sequencing the topics in the existing courses MA 3329 and MA 3330 so that the courses can be taken independently. In particular, each course will meet PDE, NCATE, and NCTM program standards on their own, and can be taken together to meet graduate school expectations. MA 3329 will be a traditional one-semester Modern Geometry course with emphasis on the axiomatic approach of Euclid and Hilbert, and MA 3330 will take a more contemporary track with emphasis on the analytic approach of Descartes, Gauss, and Riemann. Neither course will be a prerequisite for the other and both may be taken for credit. Old Course Title: Modern Geometry II New Course Title: Non-Uniform Geometries Course Description for Catalog (limit to four sentences): A study of the modern geometries leading up to the geometry of manifolds. Topics include: Euclid’s “algebraic” propositions, Descartes’ analytic geometry, the analytic approach to Euclidean geometry, Euclid’s and Hilbert’s axioms as theorems in analytic geometry, Euclid’s Fifth Postulate and the birth of non-Euclidean geometry, Descartes’ lost manuscript and the angle deficit, angle deficit and curvature, the polyhedral Gauss-Bonnet theorem, paper models of curved surfaces, and an introduction to Gaussian curvature and Riemannian geometry. MA 3329 and MA 3330 may both be taken for credit, and either course can be taken before the other.
Prerequisites: (Courses which MUST be completed prior to taking this course) MA 3260 – Discrete Structures or permission of instructor.
Describe any student enrollment restrictions (limited to majors in program XXX, restricted from majors in program XXX, etc.) The new courses are less restrictive than the old. MA 3329 may be taken before MA 3330, and either may be taken to satisfy program requirements.


8. New Course Request – MA 3306 History of Mathematics from Calculus to Computers
Purpose and Nature of Course: This is one of two new courses being developed to take the place of MA 3304 History and Philosophy of Mathematics. The two courses will be independent of each other with only a small overlap in material (essentially one chapter). They may be taken in either order, and either one will satisfy the PDE, NCATE, and NCTM standards. Both may be taken for credit. Course Description for Catalog (limit to four sentences): An in-depth study of the chronological development of facets of mathematics beginning with the development of Calculus and continuing to the present day. The historical background of each facet is integrated with experience in mathematical study and application. Emphasis is placed on great mathematicians, their contributions, and their methods of reasoning, including the contributions of underrepresented groups and diverse cultures. Concepts of number, number systems, and the nature of axiomatic reasoning are also covered. Co-requisite: MA 3260 Describe any student enrollment restrictions (limited to majors in program XXX, restricted from majors in program XXX, etc.) None – this course or MA 3305 will be required for all BSE majors and may be taken as an upper –division elective for any Mathematics program. The course will be open to anyone with the co-requisite.

 

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