MATH 1151 -- Changes

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.
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:

  • They explicitly help students understand what liberal education is, how the content and the substance of this course enhance a liberal education, and what this means for them as students and as citizens
  • They employ teaching and learning strategies that engage students with doing the work of the field, not just reading about it.
  • They include small group experiences (such as discussion sections or labs) and use writing as appropriate to the discipline to help students learn and reflect on their learning.
  • They do not (except in rare and clearly justified cases) have prerequisites beyond the University´┐Żs entrance requirements.
  • They are offered on a regular schedule.
  • They are taught by regular faculty or under exceptional circumstances by instructors on continuing appointments. Departments proposing instructors other than regular faculty must provide documentation of how such instructors will be trained and supervised to ensure consistency and continuity in courses.

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>