MAT314 Algebra and Number Systems is an advanced mathematics course. Individual professors will design their own syllabi and final exam. The course and major outcomes will be assessed on the final exam.
MAT314 is a required course for all math majors.
This course will be assessed by the professor using his own final and following his own syllabus.
MAT314 Course Outcomes [assessed using the problems in the brackets]:
1. Perform symbolic calculations involving matrices and permutations (as part of math objective A)
2. State and apply defns and thms concerning groups, cosets, and subgroups (as part of E)
3. State and apply defns and thms related to homomorphisms (as part of E)
4. State and apply defns and thms related to rings and fields (as part of E)
5. Prove mathematical statements about equivalence relations/groups (as part of G)
Math Major Outcomes incorporated into MAT314 [assessed using problems in the brackets]:
A. Perform numeric and symbolic computations
E. State and apply mathematical definitions and theorems
G. Construct and present a rigorous mathematical argument
The plan was to assess this class in Fall 2011 however the professor teaching the course had an injury. So this course will be assessed in the Fall of 2012.
Observations before Data Analysis: This is one of the most advanced courses required for the major. Some of the class will have already taken a proving course before and will handle the proofs well. Others are learning the subject for the first time and will need to take a second proving course before fully mastering this skill.
Data Analysis: A spreadsheet with a listing of each problem on the final and how many students completed each problem correctly. Different problems have been assigned to test different course and major outcomes. Scores are then computed on the spreadsheet, by taking the average number of students correct per question testing that outcome.
Conclusions:
Students performed the best on Course Outcomes 1 and 3. Course Outcome 1 is an essential component of the course and a strong performance is expected. It is more surprising that the students performed well on Course Outcome 3, however this is perhaps because more challenging proofs addressing this outcome were not required on the exam. A proof was required on a problem assessing course outcome 4 and, not surprisingly, students had a low performance on this outcome. Students did reasonable well on Course Outcomes 2 and 5 demonstrating a mastery of key topics in this course. The students performed less well on the major outcomes: they did alright on the first major outcome, less well stating the challenging definitions in this course, and least well on the proofs. However, as stated before data analysis, the students have a second required math major course which covers proofs.