Recommendations for Prerequisites and Admissions: Science
Walter Whiteley, York Representative, COU Mathematics Review Task Force.
Context for prerequisites:
1. We have the same end point in mind for the students completing first year calculus
and linear algebra, for the key MATH courses (First and Second courses in calculus:
1013, 1014; 1300, 1310; first course in Linear Algebra: 1021);
2. Some detailed discussions will be required around end point for service courses, but
we anticipate the same end point for: (General math, including calculus for Life
Sciences: 1505; Service course in Linear Algebra: 1025, Discrete Math for
Computer Science: 1019).
3. There is concern that there will not be a large enough pool of students with Calculus
and Vectors for all programs desiring this background.
With these endpoints in mind; there are some basic prerequisite recommendations:
4. We will need a revised version of MATH 1515 (coverage of high school calculus
content) as a bridge course which will cover the content of the new high school
course: Calculus and Vectors;
5. Calculus and Vectors, or this bridge course, should be a prerequisite for Math 1013
and Math 1300 (First Courses in Calculus for Sciences, and for Mathematics and
Computer Science).
6. In order to permit students who arrive without calculus and vectors to ‘catch up’ by
the end of the first semester, we recommend creation of a combined double course for
Math 1515 and 1300 (or 1515 and 1013) [High School Calculus and first university
course in Calculus) : 6 credits, 6 hours a week, two grades, probably two final exams,
common final exams with the sections of the two distinct courses.
7. We should investigate whether the bridge course (Math 1515) can be offered in
August, to entering students, as a bridge course. This would just be an additional
option for catching up.
8. Math 1505 (Math for the Life Sciences: terminal for most students) should continue
to have One Grade 12 U Math as a prerequisite. Need to debate whether to add Grade
11 U functions, since the modified Grade 11 U/C is a weaker course (can be
followed by Grade 11 U both for credit).
9. Linear Algebra 1021 will not need Calculus and Vectors as a prerequisite, but
multivariable calculus 2310 and 2015 will implicitly have this, or equivalent, as
prerequisite. Perhaps Advanced Functions should be a prerequisite for 1021?
Otherwise it should be one Grade 12 U course, plus Grade 11U Functions (translating
the current prerequisites).
10. Need to confirm prerequisites for the fast Survey Course of Linear Algebra1025
(service of engineering, physics, not for math majors). This courses rushes through
vectors and linear algebra content, and may need Vectors content of either Calculus
and Vectors or Math 1515 as a head start.
11. There will be significant problems for discrete mathematics course such as MATH
1019 for Computer Science. The curriculum content in discrete mathematics
continues to dwindle, and the processes of reasoning, and writing mathematics are
also being reduced (relative to Geometry and Discrete Math). This requires direct
discussions with Computer Science, who find Discrete Mathematics as a more urgent
first year issue than calculus (which can be delayed into second year).
Admissions consequences of first year prerequisites:
Ist draft of Recommendations.
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No program should be completely closed to students who do not have Calculus and
Vectors, as there will be a bridging course. (Some students in small schools may not
have access to Calculus and Vectors.) All such students will need Advanced
Functions as an entrance requirement – and an alert that they will need an ‘extra’
course to catch up. This may be an exceptional arrangement - or a common
pathway.
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Clearly many students and programs will benefit from having Calculus and Vectors at
time of entrance. Where programs are tight for time in first year, this should be an
admissions requirement. Students following the bridging course will need the
option of 3 more credits in the fall for this course or the chance to start University
calculus in January, and catch up by the following fall.
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Programs Requiring MATH 1013 (Calculus I, including some integration), and
MATH 1025 (fast survey of Linear Algebra) should strongly encourage students to
have Calculus and Vectors at entrance.
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Therefore, engineering may need to add Calculus and Vectors as an admissions
requirement.
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We need to communicate to students that for programs requiring calculus the only
options are: take calculus and vectors in high school or take it first semester here.
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We are recommending that Math programs not require Calculus and Vectors – just
strongly recommend it (with the information on what happens next, as above).
Similar recommendations also seem appropriate for physics, ESSE, chemistry.
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Admissions requirements for Biology, Kinesiology (Science), Psychology (Science),
and Science and Technology Studies require further discussions about the anticipated
endpoint and the prerequisites for 1505.
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Computer Science will need to examine the balance of completing discrete
mathematics, completing calculus, and recruitment, to determine new admissions
requirements.