Fri Mar 26 10:52:57 2010
Catalog Description: |
New:
Properties
of trigonometric functions and their inverses, including graphs and
identities, with applications; polar coordinates, equations, graphs;
complex numbers, complex plane, DeMoivre's Theorem; conic sections;
systems of linear equations and inequalities, with applications;
arithmetic and geometric sequences and series Old: Algebra, analytic geometry, trigonometry, complex numbers, beyond usual coverage in three-year high school mathematics. |
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Course Equivalency: |
New:
Math 1155 Old: No course equivalencies |
Editor Comments: |
New:
<no text provided> Old: In last update, line in prerequisite concerning not granting credit if certain courses already taken was left out by mistake. [added to PS note field, course notes sequence nbr 3:] Credit will not be granted if credit has been received for: Math 1155 |
Proposal Changes: |
New:
New material included so that it can be submitted for the Lib Ed Mathematical Thinking requirement Old: Only change in prerequisite--one line. |
Faculty Sponsor Name: |
New:
Lawrence Gray (Director of Undergrad Studies) Old: David Frank |
Faculty Sponsor E-mail Address: |
New:
gray@math.umn.edu Old: frank@umn.edu |
Student Learning Outcomes: |
* Student in the course:
- Can identify, define, and solve problems
New:
Please explain briefly how this outcome will be addressed in the course. Give brief examples of class work related to the outcome. Problem solving is at the heart of any mathematics course. In this course some problems would involve purely mathematical problems like deriving an unfamiliar trigonometric identity from other identities already discussed in class or showing that a certain geometric theorem about triangles can be proved using trigonometry. Other problems involve taking a real world situation like the surveying problem, identifying the mathematically relevant aspects, defining appropriate mathematical variables and relations, and then solving the resulting mathematics problem. How will you assess the students' learning related to this outcome? Give brief examples of how class work related to the outcome will be evaluated. Practically every homework assignment, quiz and examination consists of problems to be solved by the students. They will get ample feedback about their progress during the semester. Old: unselected |
Requirement this course fulfills: |
New:
MATH
- MATH Mathematical Thinking
Old: |
Criteria for Core Courses: |
Describe how the course meets the specific bullet points for the proposed core
requirement. Give concrete and detailed examples for the course syllabus, detailed
outline, laboratory material, student projects, or other instructional materials or method.
Core courses must meet the following requirements:
New: Precalculus II (Math 1151) covers topics in algebra, analytic geometry, and especially trigonometry which are of intrinsic mathematical interest, have important applications in science and everyday life, and which are needed for a full understanding of calculus. The course does not require previous background beyond three years of high school math, consistent with the University entrance requirement. The course develops in the students a real understanding of the symbolic language of mathematics, giving them ample opportunity to see how mathematics is done by mathematicians and to engage in that same work by solving problems for themselves. In this way, they see how abstract mathematical concepts can find applications in the real world. An important component of a liberal education is an appreciation of mathematics as a body of thought which has been developed over the millennia, both for aesthetic reasons and to solve concrete problems. The heart of Math 1151 is Trigonometry. As the study of triangles, trigonometry dates back to the earliest civilizations in Egypt and Mesopotamia, yet its modern form was acquired in 17th and 18th century Europe. Math 1151 presents simple geometrical problems, such as using surveying to find the height of a pyramid, and solves them with sophisticated mathematical formulas involving trigonometric functions like sine, cosine and tangent. The student sees both the fundamental nature of the questions and the usefulness of abstract reasoning in finding elegant and efficient solutions. In the TA discussion sessions, students have opportunities to engage in problem solving with their peers. Finally, the course addresses the objectives of the mathematical thinking core. The students are required to master mathematical language, such as the symbolic formulas expressing trigonometric identities. Some of these formulas are of great mathematical beauty -- a notable example being Euler¿s famous formula (e^(i pi) + 1 = 0) relating the 5 most important numbers in mathematics. They use mathematics to solve concrete problems like the surveying problem and also problems involving time-periodic phenomena like wave motion. The course is taught by a combination of regular faculty and adjunct faculty with on-going appointments, or by experienced grad students or postdocs who act under close supervision by regular faculty. Every semester, the final exam is a departmental exam that is given in common to all sections, in order to ensure consistency. Old: <no text provided> |
Provisional Syllabus: |
Please
provide a provisional syllabus for new courses and courses in which
changes in content and/or description and/or credits are proposed that
include the following information: course goals and description;
format/structure of the course (proposed number of instructor contact
hours per week, student workload effort per week, etc.); topics to be
covered; scope and nature of assigned readings (texts, authors,
frequency, amount per week); required course assignments; nature of any
student projects; and how students will be evaluated. The University policy on credits is found under Section 4A of "Standards for Semester Conversion" at http://www.fpd.finop.umn.edu/groups/senate/documents/policy/semestercon.html . Provisional course syllabus information will be retained in this system until new syllabus information is entered with the next major course modification, This provisional course syllabus information may not correspond to the course as offered in a particular semester. New: (This is an actual syllabus from a recent semester, modified to include a Lib Ed statement) Mathematics 1151 (Precalculus II) Instructor: Gennady Lyubeznik Office: Vincent Hall 259, 624-7014 Prerequisites: 3 and a half years high school math, or C- in MATH 1051, or placement exam. Required text: Precalculus 8th Edition by Sullivan, Prentice Hall. Course content: This course is the second in a two-course sequence covering the content of a standard precalculus course. We will cover most of Chapters 6 - 8 and some sections of Chapters 9 - 12. Liberal Education Requirement: This course satisfies the Mathematical Thinking Core objective of the University¿s liberal education requirement. An important component of a liberal education is to develop a working appreciation of mathematics as a body of thought which has been developed both for aesthetic reasons and to solve concrete problems. This course offer ample opportunity to develop such an appreciation. Problem solving will be a crucial component of the course. Developing your ability to translate real world problems into mathematics and to solve them using the mathematical techniques described in the course is an important goal. Homework: Homework will be assigned in class every day and the assignment will be posted on the course page. Homework will not be collected and graded. Yet doing homework is absolutely indispensable for success in the course. Quizzes: A quiz will be given every Thursday starting January 31. It will be based on the homework assigned during the preceding week. You cannot make up a quiz. Two lowest quiz scores will be dropped. Exams: There will be three midterm exams in class on Fridays, February 22, March 28 and May 2. There will be a final exam on Monday, May 12, 1:30 - 4:30pm, room to be announced. Make up exams: Will be allowed only under truly exceptional circumstances. You must notify the lecturer, not the TA, at least a week in advance. Calculators: Basic scientific calculators are allowed in exams and quizzes. These are calculators that can evaluate trigonometric, exponential and logarithmic functions. Graphing calculators or calculators that can do symbolic manipulations will not be allowed during exams and quizzes. Final grade: Quizzes count for 25%, each of the midterm exams for 15% and the final exam for 30%. Drop date: Any course may be dropped without permission before the end of the eighth week (March 17). Starting March 18, permission will be needed. The later the course is dropped, the more it costs. If a course is dropped before the end of the second week, no mention of that course will appear on the transcript, otherwise the student will receive a "W". Lecture date Quiz date Homework assignment Week 1 Wednesday, January 23 Thursday, January 31 Section 6.1, Angles and their measure Homework: #11 - 15, 17 - 21, 26, 30, 42, 44, 47 - 50, 61, 65 Friday, January 25 Thursday, January 31 Section 6.1 (continued) Homework: #71 - 74, 79, 81, 87, 91, 92, 93, 97, 99, 100, 102, 106 Week 2 Monday, January 28 Thursday, February 7 Section 6.2, Trig functions, unit circle approach Homework: #1 - 6, 12, 20, 23, 30, 46, 51, 52, 54, 68, 80, 85, 93 Wednesday, January 30 Thursday, February 7 Section 6.3, Properties of the trig functions Homework: #11, 15, 25, 27, 31, 35, 39, 41, 43, 49, 51, 57 Friday, February 1 Thursday, February 7 Section 6.3 (continued) Homework: #59, 67, 69, 75, 77, 79, 81, 85 Week 3 Monday, February 4 Thursday, February 14 Section 6.4, Graphs of the sine and cosine functions Homework: #1 - 8, 11, 23, 25, 35, 37, 43, 45, 51, 53, 57, 59 Wednesday, February 6 Thursday, February 14 Section 6.4 (continued) Homework: #67, 69 Section 6.5, Graphs of the tangent, cotangent, cosecant, and secant functions Homework: #1 - 15, 17, 19, 21, 23, 33, 37 Friday, February 8 Thursday, February 14 Section 6.5 (continued) Homework: #25, 27, 29, 31 Week 4 Monday, February 11 Thursday, February 21 Section 6.6, Phase shift; sinusoidal curve fitting Homework: #3, 5, 7, 9, 11, 13, 15, 17, 19, 21 Wednesday, February 13 Thursday, February 21 Section 7.1, The inverse sine, cosine, and tangent functions Homework: #13, 15, 17, 19, 21, 23, 25, 27, 35, 37, 39, 43, 51, 53, 55, 59, 61, 65 Friday, February 15 Thursday, February 21 Section 7.3, Trigonometric identities Homework: #13, 15, 17, 19, 21, 25, 27, 33, 35, 39, 47, 61, 71 Week 5 Monday, February 18 Thursday, February 28 Section 7.4, Sum and difference formulas Homework: #9, 19, 23, 27, 31, 37, 45, 61, 63, 73 Wednesday, February 20 Thursday, February 28 Section 7.5, Double-angle and half-angle formulas Homework: #7, 9, 27, 43, 47, 53, 59, 61, 69 Friday, February 22 Thursday, February 28 Midterm Week 6 Monday, February 25 Thursday, March 6 Section 7.7, Trigonometric equations (I) Homework: #7, 9, 15, 21, 27, 29, 31, 33, 35, 37, 39, 47, 51 Wednesday, February 27 Thursday, March 6 Section 7.8, Trigonometric equations (II) Homework: #5, 9, 11, 17, 23, 25, 33, 37, 41, 47, 49 Friday, February 29 Thursday, March 6 Section 8.1, Applications involving right triangles Homework: #9, 17, 19, 23, 27, 29, 39, 49, 51, 55, 63 Week 7 Monday, March 3 Thursday, March 13 Section 8.2, Applications of the law of sines Homework: #9, 11, 13, 15, 23, 25, 27, 29, 31, 33 Wednesday, March 5 Thursday, March 13 Section 8.3, Applications of the law of cosines Homework: #9, 15, 21, 31, 33, 35, 39 Friday, March 7 Thursday, March 13 Section 8.4, Area of a triangle Homework: #5, 7, 11, 9, 13, 23, 33, 35, 39 Week 8 Monday, March 10 Thursday, March 20 Section 9.1, Polar coordinates Homework: #1- 10, 11, 13, 15, 17, 19, 27, 31, 39, 51, 55, 59, 69, 75 Wednesday, March 12 Thursday, March 20 Section A.7: Quadratic equations with complex numbers Homework: #13, 19, 27, 41, 49, 53, 59, 73, 85, 87 Friday, March 14 Thursday, March 20 Section 9.3, The complex plane, DeMoivre's Theorem Homework: #11, 13, 23, 31, 33, 35, 37, 39, 41, 45, 47, 51, 53, 55, 57, 59 Week 9 Monday, March 24 Thursday, April 3 Section 4.5, The real zeroes of polynomial functions Homework: #11, 15, 33, 35, 41, 45, 47, 51, 57, 63 Wednesday, March 26 Thursday, April 3 Section 4.5 (continued) Homework: #57, 61 Friday, March 28 Thursday, April 3 Midterm Week 10 Monday, March 31 Thursday, April 10 Section 4.6, Complex zeroes and the fundamental theorem of algebra Homework: #7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 31, 33, 35 Wednesday, April 2 Thursday, April 10 Section 10.1-10.2, Intro to conics, parabolas Homework: #11, 13, 19, 21, 27, 29, 37, 39, 47, 57, 59 Friday, April 4 Thursday, April 10 Section 10.4, Hyperbolas Homework: #17, 19, 27, 29, 37, 39, 41, 47, 51, 53 Week 11 Monday, April 7 Thursday, April 17 Section 10.3, Ellipses Homework: #17, 19, 21, 27, 29, 37, 39, 47, 53, 55, 59 Wednesday, April 9 Thursday, April 17 Section 10.2, Back to parabolas Homework: #49, 51, 53 Section 10.3, Back to Ellipses Homework: #49, 51 Section 10.4, Back to hyperbolas Homework: #55, 57, 59 Friday, April 11 Thursday, April 17 Section 11.1, Systems of linear equations, substitution and elimination Homework: #7, 9, 19, 25, 29, 35, 37, 39, 55 Week 12 Monday, April 14 Thursday, April 24 Section 11.1 (continued) Homework: #41, 43, 45, 49, 53, 69, 73 Wednesday, April 16 Thursday, April 24 Section 11.2, Systems of linear equations, matrices Homework: #7, 11, 15, 17, 19, 21, 23, 27, 29, 31, 33 Friday, April 18 Thursday, April 24 Section 11.2 (continued) Homework: #37, 39, 47, 51, 53, 57, 61, 63, 69, 73, 77, 83 Week 13 Monday, April 21 Thursday, May 1 Section 11.8, Linear programming Homework: #3, 5, 7, 9, 11, 13, 15 Wednesday, April 23 Thursday, May 1 Section 11.8 (continued) Homework: #19, 21, 23, 27 Friday, April 25 Thursday, May 1 Section 12.1, Sequences Homework: #11, 13, 17, 19, 23, 27, 29, 35, 37, 43, 51, 53, 61, 63, 73, 75 Week 14 Monday, April 28 Thursday, May 8 Section 12.1 (continued) Homework: #61, 71, 77, 79 Section 12.2, Arithmetic sequences Homework: #3, 5, 7, 9, 11 Wednesday, April 30 Thursday, May 8 Section 12.2 (continued) Homework: #13, 15, 19, 21, 25, 27, 31, 33, 35, 39, 45, 47, 49 Friday, May 2 Thursday, May 8 Midterm Week 15 Monday, May 5 Section 12.3, Geometric sequences and series Homework: #9, 11, 17, 19, 21, 23, 27, 33, 35, 41, 45, 49, 53, 55, 57, 59 Wednesday, May 7 Section 12.3 (continued) Homework: #67, 69, 71, 73, 75, 77, 87 Friday, May 9 Review The final is Monday, May 12, 1:30-4:30 in Anderson Hall, in the following rooms: Discussion section Room number Dis011, 013 rm 230 Dis012, 014, 015 rm 210 Dis021, 025 rm 250 Dis022, 023, 024 rm 270 You must bring your ID and know your discussion section number Old: <no text provided> |