The following table defines Department of Mathematical Sciences Learning Goals O1-O14. We also show the alignment between Departmental goals and General Education goals 1 and 2 (see http://www.ugs.udel.edu/gened/). In the list
Students in Mathematical Science degree programs are expected to achieve General Education learning goals 3-10 and the oral communication part of goal 1 via breadth requirements.
O1: |
(G1/Q, G2) Student understands basic properties of functions including limits, continuity and differentiability, and can answer questions about these properties applied to polynomials, trigonometric functions, powers, roots and piecewise combinations of these basic elements. |
O2: |
(G1/Q, G2) Student can differentiate functions composed of basis elements including polynomials, trigonometric functions, exponentials, logarithms, rational functions and piecewise functions, using techniques such as the product rule, quotient rule, chain rule and implicit differentiation. |
O3: |
(G1/Q, G2) Student can rigorously analyze a function to connect an equation with its graph. This includes location of roots and asymptotes, local minima and maxima and inflection points. |
O4: |
(G1/Q, G2) Student can apply concepts in differential calculus to word problems in a variety of elementary settings. Possible settings include business, the physical sciences or the biological sciences. Student can apply concepts in differential calculus to related problems such as curve sketching, optimization, Newton's method or linearization. |
O5: |
(G1/Q, G2) Student can solve a linear algebraic system, and understands and can apply equivalent statements concerning the solution of linear algebraic systems. |
O6: |
(G2) Student can recognize and state a precise mathematical definition. Student can recognize and state a precisely phrased mathematical theorem. |
O7: |
(G2) Student can reproduce a theorem and apply the theorem to problems. Student has the ability to construct simple proofs. |
O8: |
(G1/Q, G2) Student can integrate compostions of elementary functions using a variety of techniques including substitution and integration by parts. |
O9: |
(G1/Q, G2) Student can manipulate infinite series using basic arithmetic on constituent terms. Student can determine whether or not a sequence or series converges using different tests including the ratio test and limit comparison tests. |
O10: |
(G1/Q, G1/IT, G2) Student can solve complex problems using mainstream mathematical software such as Maple, Mathematica, Magma or Matlab. |
O11: |
(G1/Q, G2) Student can solve basic probabilistic problems involving basic combinatorial concepts. Student can determine expectations and variances given continuous or discrete probability distributions. |
O12: |
(G2) Student can acquire new knowledge independently from another source such as a journal article or a book. |
O13: |
(G1/W, G2) Student can write about mathematical topics at an advanced undergraduate level. |
O14: |
(G2) Student can integrate functions on curves, surfaces and solids. Students can use differential operators such as grad, div and curl, and apply Stoke's Theorem and the Divergence Theorem to compute integrals. |
L: |
Material is provided in lectures. |
Hw: |
Material is exercised in problem sets. |
Ex: |
Performance is measured on exams. |
P: |
Performance is measured through projects or portfolios. |
R: |
Material is reviewed or reinforced. |
Items in bold indicate that necessary preparation for the learning goal is provided.
Course |
O1 |
O2 |
O3 |
O4 |
O5 |
O6 |
O7 |
O8 |
O9 |
O10 |
O11 |
O12 |
O13 |
O14 |
| Math 117 | L Hw Ex | L Hw Ex | L | |||||||||||
| Math 210 | L Hw Ex | L Hw Ex | ||||||||||||
| Math 241 | L Hw Ex | L Hw Ex | L Hw Ex | L Hw Ex | L Hw | L | L Hw Ex | |||||||
| Math 242 | R | R | R | L Hw Ex | L Hw Ex | L Hw | ||||||||
| Math 243 | R | L R | L | |||||||||||
| Math 245 | L Hw Ex | L Hw Ex | ||||||||||||
| Math 302 | R | R | R | L Hw Ex | R Hw | |||||||||
| Math 308 | L Hw | |||||||||||||
| Math 315 | R L Hw Ex | |||||||||||||
| Math 349 | L Hw Ex | L Hw Ex | L Hw Ex | R Hw | ||||||||||
| Math 380 | L Hw | |||||||||||||
| Math 401 | R | R | R | R | R | |||||||||
| Math 426 | R | R | ||||||||||||
| Math 451 | R | R | ||||||||||||
| Math 350 | R | L Hw Ex | ||||||||||||
| Math 460 | L Hw | |||||||||||||
| Math 503 | R | R | R | R | R | |||||||||
| Math 508 | R | R | R | R | R | R | R | |||||||
| Math 512 | R | R | R | R | R | R | R | R | R | P | P | |||
| Math 518 | R | R | R | R | R | R | R | R | R | |||||
| Math 530 | L Hw | |||||||||||||
| Math 535 | R | R | R | R | R | R | R | |||||||
| Math 549 | R | R L | P | P |