MATH 1001 -- Changes

Fri Mar 26 10:47:29 2010

Effective Term: New:  1109 - Fall 2010
Old:  1089 - Fall 2008
Catalog
Description:
New:  Introduction to the breadth and nature of mathematics and the power of abstract reasoning, with applications to topics that are relevant to the modern world, such as voting, fair division of assets, patterns of growth, and opinion polls.  
Old:  Breadth of mathematics, its nature/applications. Power of abstract reasoning.
Course
Prerequisites
for Catalog:
New:  3 yrs high school math or placement exam or grade of at least C- in PSTL 731 or 732
Old:  3 yrs high school math or placement exam or grade of at least C- in GC 0731
Proposal Changes: New:  The course is the same, but an update was needed for re-certification for the Mathematical Thinking liberal education requirement.
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Faculty
Sponsor Name:
New:  Lawrence Gray (Director of Undergrad Studies)
Old:  
Faculty
Sponsor E-mail Address:
New:  gray@math.umn.edu
Old:  
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.

The primary focus of this course is to use mathematics to solve problems that arise in everyday life, using a three-step process: (i) recognize when a problem is amenable to a particular type of mathematical treatment; (ii) solve the resulting mathematical problem using techniques learned in the course; (iii) interpret the result in the context of the original everyday situation. For example, the everyday problem might be how to interpret the result of an election involving three or more candidates if no candidate receives a clear majority of the votes. Students learn various mathematical approaches to solving this problem and they learn how to evaluate the strengths and weaknesses of these approaches according to precise mathematical criteria. Another example: Students are presented with a problem involving the fair division of an inheritance that consists of various items of property that cannot be easily sold nor easily broken apart into pieces, and the different heirs do not necessarily value the items in the same way. Students learn mathematical methods for arriving at a fair division of the property among the heirs, and they learn how to apply mathematical criteria for fairness.

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.

All of the homework and exam questions are either stated as problems that arise in everyday life, or they are directly related to such problems. Students must provide complete solutions to these problems.

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- Have acquired skills for effective citizenship and life-long learning

New:

Please explain briefly how this outcome will be addressed in the course. Give brief examples of class work related to the outcome.

Quantitative literacy is a key component in good citizenship, since many public issues cannot be properly addressed without at least some numerical work. Many of the topics in this course relate directly to such issues. For example, students learn to use some basic statistical quantities to compare and evaluate data arising from opinion polls or surveys. Quantitative literacy also opens the door to learning in many areas that would be otherwise inaccessible. Throughout the course, students learn to reason quantitatively about data (means, standard deviations, the bell-shaped curve), shapes (fractals, golden rectangles, patterns), human interactions (voting, fair division), and certain dynamical situations (exponential growth), all of which can lead to whole worlds of interesting ideas.

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.

Students naturally become more quantitatively literate as they encounter mathematical ideas and symbols, apply mathematical formulas to a variety of problems, and communicate their results. The quality of their work on homework and exams correlates well with their level of quantitative literacy.

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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:
Learning to reason carefully is an important part of any liberal education, and there are several different types of reasoning.  This course helps students learn when quantitative reasoning is appropriate, and how to reason quantitatively in a variety of settings.  They will do what mathematicians do: identify problems, clarify important issues in terms of precise mathematical concepts, and solve  problems using mathematical reasoning and mathematical procedures. The course includes a small group recitation session (20-30 students) once a week, where students discuss problem solving techniques and practice using them, supervised by a graduate teaching assistant.  There are three hours of lectures each week, usually taught by a regular faculty member, or by an instructor with a continuing appointment. On rare occasions, we trust an experienced graduate student to teach the course, under close supervision.  The prerequisites for the course are the same as the prerequisites for entering the university.  The course is taught every semester.  

Students continually use high school algebra and geometry as part of their toolbox for solving problems in the course.  They encounter many new formulas and definitions, requiring them to comfortably read and use mathematical symbols and terminology in significant ways.  Some of the topics in the course are motivated by very concrete problems that arise in everyday life, while others are motivated simply by the sheer beauty of the underlying mathematical ideas.  Many of the topics exhibit both sides of mathematics: its intrinsic beauty and its usefulness.
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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:  (Actual syllabus from a previous semester, modified to include a Lib Ed statement)

Math 1001 Syllabus Spring 2008

Lecturer and TA: Professor Dennis Stanton, Vincent Hall 253, 624-7544, TA: Ben Rosenfield, Vincent Hall 504, 624-1543

Time and Location: Lecture: 11:15-12:05 EE/CSci 3-230, Recitation: Th 10:10, KoltH138, Th 11:15, EE/CS 3-115, Th 12:15 KoltH 138

Office Hours MWF 10:10-11:00

Text: Excursions in Modern Mathematics, 6th edition, by P. Tannenbaum

e-mail address: stanton@math.umn.edu

web address: http://www.math.umn.edu/~stanton

Liberal Education:  This course satisfies the Mathematical Thinking Core portion of the Liberal Education requirements at the University of Minnesota.  One important aspect of a liberal education is learning different ways to think about and find solutions to problems that arise in our daily interactions, in our work, and in our society.  When quantities, data, or geometric structures are involved, mathematical reasoning is crucial in the analysis of such problems.  This course will introduce you to a quantitative, logical way of thinking known as Mathematical Thinking, and it will require you to use it to solve problems in a variety of interesting situations, as indicated in the weekly list of topics.  

Mathematical Prerequisites: You should have had at least three years of high school mathematics.

Topics: We will cover Chapters 1-6, 10,12,14,15,16 of the textbook. This includes mathematics applied to social sciences, examples of algorithms in graph theory, population growth and elementary discrete mathematics. This course emphasizes mathematical reasoning over technical expertise. You should read the preface of your textbook.

Grading and Exams: There will be an 3 in-class exams and a final exam. All students failing all 4 exams automatically fail the class. Otherwise your grade will be determined by the following weights:

   * Final exam 40%,
   * Mid-Term I 15%,
   * Mid-Term II 15%
   * Mid-Term III 15%
   * Recitation grade 15%

Solutions to the homework problems will be posted on our web page each Thursday. Late homework is NOT accepted. You may work together on the homework problems, but must write up your solutions in your own words. Your solutions should be written clearly in complete sentences. You may bring any books, notes, calculators you wish to the exams. You are expected to attend lectures and recitations. I expect to learn your names and will call on you during class. You should prepare for class in advance by reading the material. If you have a borderline grade, the final exam takes precedent.

Absence from exams: Missing an exam is permitted only for the most compelling reasons. You should obtain my permission in advance to miss an exam. Otherwise you will be given a 0. If you are excused from taking an exam, you will be given an oral exam, or your other exam scores will be prorated.

Official University Grading Standards:

A achievement that is outstanding relative to the level necessary to meet course requirements.
B achievement that is significantly above the level necessary to meet course requirements.
C achievement that meets the course requirements in every respect.
D achievement that is worthy of credit even though it fails to meet fully the course requirements.
S The minimal standard for S is to be no lower than C-. The instructor or department must inform the class of this minimal standard at the beginning of the course.
F (or N) Represents failure (or no credit) and signifies that the work was either (1) completed but at a level of achievement that is not worthy of credit or (2) was not completed and there was no agreement between the instructor and the student that the student would be awarded an I.
I (Incomplete) Assigned at the discretion of the instructor when, due to extraordinary circumstances, e.g., hospitalization, a student is prevented from completing the work of the course on time. Requires a written agreement between instructor and student.

Official University Statement on Academic Dishonesty: Academic dishonesty in any portion of the academic work for a course shall be grounds for awarding a grade of F or N for the entire course.

Official University Statement on Credits and Workload Expectations: For undergraduate courses, one credit is defined as equivalent to an average of three hours of learning effort per week (over a full semester) necessary for an average student to achieve an average grade in the course. For example, a student taking a three credit course that meets for three hours a week should expect to spend an additional six hours a week on coursework outside the classroom.

My Statement on Incompletes, S/N: The grade ``I" is assigned only when a student has satisfactorily (a C- grade or better) completed all but a small portion of the work for the course, and has made prior arrangements to complete the work. This means, for example, if you quit attending class after the second exam, and then request an ``I" in the tenth week, your request will be denied. You will fail the course. To obtain an S, you need at least a C- grade.

Scholastic Conduct: Each student should read his/her college bulletin for the definitions and possible penalties for cheating. During the exam you must do your own work. Students suspected of cheating will be reported to the Scholastic Conduct Committee for appropriate action.

Complaints: You can address complaints about your lecturer to the Undergraduate Head, Professor David Frank, Vincent Hall 115.

Messages: If for some reason you need to leave an urgent message, you can do so at the School of Mathematics, 625-4848. You may also post anonymous suggestions and comments on our class web page.

Course Outline (The problems are due on Thursday.)

W Jan 23- W Jan 30  Chap. 1, The Mathematics of Voting (The Paradoxes of Democracy)
 Homework:  #2,14,20,32,35,49,62,68,78
F Feb. 1-W Feb. 6  Chap. 2, The Mathematics of Power (Weighted Voting)
 Homework:  #2,7,12,22,24,29,40,43,46,56,67,75
F Feb. 8-W Feb. 13  Chap. 3  (not 3.3-3.5), The Mathematics of Sharing (Fair-Division Games)
 Homework: #2,6,11,14,17,52,56,59,74,78
F Feb. 15-W Feb. 20 Chap. 4, The Mathematics of Apportionment (Making the Rounds)
 Homework: #1,6,11,16,20,23,28,33,38,43,48,58,65
F Feb. 22 Exam 1 over Chap. 1-4

M Feb. 25- W Feb. 27 Chap. 5, The Mathematics of Getting Around (Euler Paths and Circuits)
 Homework: #2,5,12,22,25,28,46,55,56,69
F Feb. 29-W Mar. 5 Chap. 6, The Mathematics of Touring (The Traveling Salesman Problem)
 Homework: #4,10,16,22,32,37,44,51,70
F Mar. 7 -W Mar. 12 Chap. 10, The Mathematics of Money (Spending It, Saving It, and Growing It)
 Homework: #2,7,16,20,25,30,37,42,56,66,68,76
F Mar. 14 Exam 2 over Chap. 5,6,10

M Mar. 24 Go over Exam 2
W Mar. 26 -W Apr. 2 Chap. 12 (not 12.4-12.5), The Geometry of Fractal Shapes (Naturally Irregular)
 Homework: #2,8,21,22,29,33,55,68
F Apr. 4-W Apr. 9 Chap. 14, Descriptive Statistics (Graphing and Summarizing Data)
 Homework: #5,6,15,16,24,28,34,56,66,70,75,80,86
F Apr. 11-W Apr. 23 Chap. 15, Chances, Probabilities, and Odds (Measuring Uncertainty)
 Homework: #5,10,14,18,24,35,46,47,48,56,65,70,74,76,78,81,85
F Apr. 25-W May 1Chap. 16, The Mathematics of Normal Distributions (The Call of the Bell)
 Homework: #2,5,11,14,16,22,26,30,32,36,37,41,50,52,56,57,62,68,72,78
F May 2 Exam 3 over Chap. 12,14,15,16

M May 4 Go over Exam 3
W May 7-F May 9 Review for Final exam
Final Exam Monday May 12, 2008 1:30-4:30 Location to be announced
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