MATH 1155 -- Changes

Wed Mar 31 09:49:12 2010

New:  Combines Math 1051 and 1151; graphs of equations and functions; polynomial and rational functions; inverses and composition of functions; exponentials and logarithms; trig functions, graphs, identities; polar coordinates; complex numbers; systems of linear equations; arithmetic, geometric sequences, series; applications
Old:  Algebra, analytic geometry, exponentials, logarithms, trigonometry, complex numbers, beyond usual coverage in three-year high school mathematics. One semester version of 1051-1151.
for Catalog:
New:  3 yrs high school math or satisfactory score on placement exam or grade of at least C- in [PSTL 731 or PSTL 732]
Old:  Satisfactory score on placement exam or grade of at least C- in [PSTL 731 or PSTL 732]
New:  Math 1031/1051/1151
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 1031, 1051, 1151
Proposal Changes: New:  Course being submitted for the Lib Ed Mathematical Thinking requirement.  Minor changes in wording, prereqs, course equivalencies, for consistency with other precalc courses.
Old:  only change in prerequisite--one line.
Sponsor Name:
New:  Lawrence Gray (Director of Undergrad Studies)
Old:  David Frank
Sponsor E-mail Address:
Student Learning Outcomes: * Student in the course:

- Can identify, define, and solve problems


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 issues, like finding the roots of a polynomial or determining the features of the graph of a rational functions. Other problems involve taking a real world situation like predicting the trajectory of a projectile or analyzing population growth and decline, requiring students to first identify the mathematically relevant aspects, then define appropriate mathematical variables and relations, and finally solve 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. Students will be challenged to develop their problem-solving skills, and they will get ample feedback about their progress during the semester.

Old: unselected

this course fulfills:
New:  MATH - MATH Mathematical Thinking
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.

This course combines Math 1051 and 1151, including all aspects of those courses that are relevant to the Mathematical Thinking Core.  The next three paragraphs contain text from the proposals for those two courses:

Math 1051 covers topics in algebra that are of intrinsic mathematical interest, have important applications in science and everyday life, and needed for a full understanding of calculus.   Although the course does not require previous mathematical background beyond high school, it develops in the students a real understanding of the symbolic language of mathematics and gives them ample opportunity to see how mathematics is done by mathematicians as the students solve problems for themselves, communicate their results, and learn how abstract mathematical concepts can find applications in the real world.  

Much of modern mathematics is founded on the algebra of equations and functions.  The first symbolic approach to equations began in the Arab world during the 9th century AD, and the concept of function was first introduced in the 14th century.  But it was the advent of calculus that made the algebra of equations and functions central to so many applications of mathematics.  That is why Math 1051 focuses on using algebra to solve equations and analyze some basic families of functions.  It helps prepare students for the kind of mathematical thinking that is central to calculus.  

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.

Math 1155 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 concerning such practical situations as interest rates, surveying, and sound waves.

Math 1155 is taught every semester, by a combination of regular faculty and adjunct faculty with ongoing appointments.  In some semesters, the lectures are also taught by experienced graduate students or postdocs, under close supervision by regular faculty.  In the TA discussion sessions, students have opportunities to engage in problem solving with their peers.  The final exam is a departmental exam, in order to ensure a consistent level of expectations.  
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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 . 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:  The following syllabus from a recent semester has been modified to include a Lib Ed statement.  In this particular sample, the names of the various topics were not included in the list of weekly assignments.  But the textbook is the same as the one used for Math 1051 and 1151, and the topic names can be found in the proposals for those courses.  

Math 1155 Syllabus Spring Semester 2010

COURSE: Intensive Precalculus

Lecture 010: MWF 2:30pm-3:20pm in Vincent Hall 20
Discussion: TR 2:30pm-3:20pm in Blegen Hall 260

LECTURER: Hye-Won Kang
Office: Vincent Hall 270C
Email: hkang (at) math (dot) umn (dot) edu
Web Page:
Office Hours: MF 1:25pm-2:15pm, W 12:20pm-1:10pm

Guowei Yu (Discussion 011)
Office: Vincent Hall 552
Email: yuxxx222 (at) math (dot) umn (dot) edu
Web Page:
Office Hours:

TEXT: Precalculus, Sullivan, Eighth edition., Pearson Prentice Hall (2008).

COURSE CONTENTS: Linear and quadratic equations and inequalities; graphs of equations; exponentials
and logarithms with applications; trigonometric functions; identities and applications;
real and zeros of polynomials; polar coordinates and DeMoivre's theorem; solutions
of systems of equations by substitution and elimination; arithmetic sequences and geometric

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.

PREREQUISITE: 3 years high school math or satisfactory score on placement test or grade of at least C-; in PSTL 731 or PSTL 732.

MIDTERM EXAMS: Three midterms will be taken in class. Chapters for each midterm is given in the
schedule of the course. You are allowed to bring one page one-sided cheat sheet during
the exam.

FINAL EXAM: All Math 1155 students are required to take a cumulative final examination covering all
the topics listed on this syllabus. The final exam is set on May 10 starting at 1:30 pm for
three hours. This time is arranged by University, and cannot be changed. Students with
conflicting exam schedules may be permitted to take an alternate final exam AFTER
the regularly scheduled exam. In the final exam, you must bring your student ID, and
are required to show it when you submit the exam. You are allowed to bring one page
two-sided cheat sheet during the exam.

SCHEDULE OF EXAMS: Exam 1: February 24, 2010 during the lecture
Exam 2: March 26, 2010 during the lecture
Exam 3: April 28, 2010 during the lecture
Final: May 10, 2010 1:30 pm-4:30 pm, Location will be announced later.

MAKE UP EXAM AND MISSED EXAM POLICY: In very emergency case only, you can ask for
a make-up exam. You must notice to the lecturer (not to a TA) at least 10 days before
the original exam date. Make-up exams will be taken before the original exam date (for
midterms). In case, you do not notice for a make-up exam and missed it, there will be
no make-up exam AT ANY CASE. When there is serious excuse you could not notice me
in advance and could not take the exam (ex. sickness with written statement, funeral,
etc), your grade will be calculated as follows: in case you miss one midterm exam, I will
average your two midterm exam scores and take 80% of the value as a missed exam score.
In case you missed two midterm exams, I will give 80% of your midterm score for the
one missed exam and will give zero point for the other missed exam. If you miss the final
exam, I do not think you can pass the course.

ATTENDANCE: The attendance is not mandatory, but is highly recommended. Based on the previous
experience, students who attend every lecture and discussion session have a very higher
tendency to get a higher score at the end.

HOMEWORK: Every Thursday, you are required to turn on your homework to your TA, which are
assigned on last Wednesday, Friday, and this Monday, before your discussion session
starts. Homework will be graded only based on the completion.

QUIZZES: Every Thursday at the end of your discussion session, you will have a quiz for 10 to 15
minutes. In the course schedule table, there are quizzes on week 2, 3, 4, 5, 7, 8, 11, 12,
13, 14, and 16 (in total 11 quizzes). Each quiz consists of two problems which are equal
or similar to homework problems. All quiz problems will be graded, and you can drop
the lowest two grades. Therefore, there is NO MAKEUP for quizzes at any situation. In
case you are not able to take it due to emergency situation, you take that grade off as a
part of two to be dropped.

CALCULATOR: During quizzes and exams, you can use a SCIENTIFIC calculator. However, using a
graphical calculator or a calculator with symbolic manipulations will be prohibited.

GRADING POLICY: Grades are based on homework, quizzes, three midterm exams, and a cumulative
final exam. Contributed portions are as follows:

Total points 50 points 90 points 300 points 300 points 740 points
(10 points each) (100 points each)
Percentage 6.8% 12.2% 40.5% 40.5% 100%

S/N GRADE: If you are registered as S/N, you will get a grade S if your letter grade is C or above,
otherwise, a grade of N.
INCOMPLETE: If you do complete the course successfully except for a very small portion due to very
extraordinary and emergency situation, you will be considered to get Incomplete. You
must have taken at least 2 midterms exams with a grade C or above to get Incomplete
with requiring to submit a written statement. If the reason to get Incomplete is because
you are behind in the course, I would recommend to drop the course, instead.

GETTING HELP: The PAL (Peer-Assisted Learning) program at SMART Learning Commons
Locations areWilson,Walter, andMagrath Halls. More information is in

will cover various topic, Math 1155 is two classes compressed into one, MATH 1051 and
MATH 1151. The below is the approximate schedule of the course which is subject to
change. The changed schedule will be updated regularly on the course web page.

1 M Jan 18 Martin Luther King Holiday
W Jan 20 1.1 24,32,36,38,61
F Jan 22 1.2 22,26,32,45,60
2 M Jan 25 1.3-1.24 (1.3) 16,26,32,50,62,66,80 (1.4) 32,42,47,51
W Jan 27 2.1-2.2 (2.1) 16,34,42,67,68 (2.2) 24,28,29
F Jan 29 2.3-2.4 (2.3) 26,32,36,42,60,63 (2.4) 18,20,22,26,49
Monday, February 1, is the last day to withdraw from the course without receiving a W
on your transcript. Also, it is the last day to change your grade option to or from
Pass/No Pass.
3 M Feb 1 2.5-2.6 (2.5) 23,24,25,34,52,60,89 (2.6) 8.(a),(b),18,21,23
W Feb 3 3.1,3.3 (3.1) 18,30,43 (3.3) 40,52,62,83
F Feb 5 3.4 6,10,12(a),(b),(c),(f),17,18
4 M Feb 8 4.1 46,50,53,54,81,82
W Feb 10 4.2 22,42,45,46,54
F Feb 12 4.3 10,12,26,27,49(a),50(a)
5 M Feb 15 4.4 5,6,11,12,29,30,51,52
W Feb 17 4.5 49,50,70,71,89,90
F Feb 19 4.5 continued
6 M Feb 22 REVIEW
W Feb 24 EXAM 1 1.1-1.4, 2.1-2.6, 3.1, 3.3-3.4, 4.1-4.5
F Feb 26 5.1-5.2 (5.1) 32,46,47,60,61,65 (5.2) 34,36,52,66,89,90
7 M Mar 1 5.3 44,56,75,80,82,103,104
W Mar 3 5.4 20,24,32,36,94,108,110,117,121
F Mar 5 5.5 46,48,58,62,79,80
8 M Mar 8 5.6 24,44,56,76,82,93,94
W Mar 10 6.1-6.2 (6.1) 44,54,72,80,95,96 (6.2) 93,94,110,117
F Mar 12 6.3 40,50,86,88,119,120
Monday, March 15, is the last day to withdraw from the course without approval of college
scholastic committee with receiving a W on your transcript.
9 M Mar 15 Spring break
W Mar 17 Spring break
F Mar 19 Spring break
10 M Mar 22 6.4 44,48,62,66,95,96
F Mar 26 EXAM 2 5.1-5.6, 6.1-6.4
11 M Mar 29 6.5 18,20,26,28,50
W Mar 31 6.6 4,8,20,24,27,28
F Apr 2 7.1-7.2 (7.1) 20,24,37,38,63,64,76(a),(b) (7.2) 26,28,59,60,79
12 M Apr 5 7.3 32,33,48,54,67,82,83
W Apr 7 7.4 22,28,32,46,61,62,76,93,94,95
F Apr 9 7.5 8,10,12,28,47,61,63,85,96
13 M Apr 12 7.7 12,16,28,33,38,55,56,61,62
W Apr 14 7.8 23,24,30,42,45,65(a),(b),(c)
F Apr 16 9.1 30,44,45,61,62,71,72,77,81
14 M Apr 19 9.3 20,28,45,46,49,50
W Apr 21 11.1 30,34,49,58,59,63,64
F Apr 23 11.6 30,42,54,58,87,88
15 M Apr 26 REVIEW
W Apr 28 EXAM 3 6.5-6.6, 7.1-7.8, 9.1, 9.3, 11.1, 11.6
F Apr 30 11.7 28,40,46,48,59,60
16 M May 3 12.1-12.2 (12.1) 55,56,74,75,89(a),(b),(c) (12.2) 42,46,47,48,55
W May 5 12.3 59,60,72,88,89,90
17 M May 10 FINAL EXAM 1:30 pm-4:30 pm, Cumulative
Old:  <no text provided>