Students in the University of Redlands' one-semester sophomore-level linear algebra course meet in a computer classroom/laboratory*, where they use MATLAB virtually every class day for computations, for formulating and testing conjectures, and for more formal in-class assignments. The students use MATLAB for almost every homework assignment from their textbook as well, mainly for computations and for checking answers, but also to explore and conjecture, and to investigate applications. In fact, students present applications of linear algebra to their classmates in groups of two or three students each. Nevertheless, we cover the traditional vector space topics, emphasizing understanding of the geometry underlying the concepts, of the techniques associated with the concepts, and of mathematical theorems and proofs, and our course serves as a transition course for students progressing from calculus to upper division mathematics courses. We describe our course, giving specific examples of computer activities and assignments and of applications of linear algebra presented by groups of students.

*Set up with an NSF ILI grant

*There is no getting out of it. Through and through the world is infected with quantity. To talk sense is to talk in quantities. . . . You cannot evade quantity. You may fly to poetry and to music, and quantity and number will face you in your rhythms and your octaves. Elegant intellects which despise the theory of quantity are but half developed. They are more to be pitied than blamed.*
- Alfred North Whitehead in The Aims of Education, 1917

*A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are
more permanent than theirs, it is because they are made with ideas.*
- G. H. Hardy

**Instructor:** Janet Beery

**Office:** Hentschke 203D

**Phone:** x3118

**Meeting Times**: Monday, Wednesday, Friday, 1 - 2:20 p.m.

**Instructor Office Hours:** Monday through Friday, 2:30 - 4 p.m.; and by appointment. I teach other courses MWF, 8:30-9:50 a.m. and MWF, 11:30-12:50 p.m., and I often have meetings at 4 p.m. Otherwise, I probably am in my office or elsewhere in Hentschke Hall; call first to make sure.

**Text:** Linear Algebra with Applications (second edition), by Gareth Williams

**Course Objectives:**

- To understand several important concepts in linear algebra, including systems of linear equations and their solutions; matrices and their properties; determinants and their properties; vector spaces; linear independence of vectors; subspaces, bases, and dimension of vector spaces; inner product spaces; linear transformations; and eigenvalues and eigenvectors;

- to apply these concepts to such real world phenomena as electrical networks, traffic flow, archeological dating, economic interdependencies, population movement, communication networks, and weather prediction;

- to learn to use the computer package MATLAB to perform matrix computations and to explore and analyze linear algebra concepts;

- to improve your ability (or to learn!) to prove mathematical theorems;

- to improve your ability to think logically, analytically, and abstractly; and

- to improve your ability to communicate mathematics, both orally and in writing.

Final % Grade Final % Grade Final % Grade 94-100 4.0/A 79-81 2.7/B- 63-66 1.3/D+ 90-93 3.7/A- 75-78 2.3/C+ 60-62 1.0/D 86-89 3.3/B+ 70-74 2.0/C 55-59 0.7/D- 82-85 3.0/B 67-69 1.7/C- 0-54 0.0/F

**Daily Homework Assignments:** There will be a homework assignment, consisting of reading and exercises, corresponding to almost every class meeting. Ideally, you should complete the reading listed for each class meeting before the class meeting; certainly, you should complete it before attempting that day's homework exercises. The exercises are due at the start of the next class period unless I say otherwise in the weekly assignment sheet or in class. Late homework will not be accepted without prior permission. Your three lowest daily homework scores will not be included in your homework average.

You are encouraged to discuss strategies for solving homework exercises with me, with tutors and with your classmates, and you certainly should check answers to computational exercises with your classmates. However, unless I say otherwise, the work you hand in must be essentially your own. A good way to help ensure this is to write up your solutions independently. Occasionally, you will earn homework points for in-class activities and presentations. In fact, at least one of your homework assignments will be a group presentation of an application of linear algebra.

**Examinations:** There will be three 100-point examinations during the semester, on approximately March 4, April 11, and May 6. In addition, there will be a 200-point final examination, part of which will focus on what we study during the last week or two of class, but most of which will be comprehensive in nature. The Office of the Registrar has scheduled the final examination for []. The instructor reserves the right to administer 10- to 20-point quizzes with at least two class days notice.

**Time Commitment:** You should expect to spend at least two hours studying outside of class for every hour spent in class. This means that for each of our 1 hour, 20 minute class sessions, you should plan to spend at least 2 hours, 40 minutes of quality time studying outside of class. Of course, if you wish to earn a grade of A or B, you may have to study more!

University of Redlands, Spring 1993

Instructor:

*Meeting Times:* Monday, Tuesday, Thursday, Friday, 10 a.m.

*Meeting Place:* By Monday, Feb. 8, we should be meeting in the newest Hentschke classroom computer laboratory, Hentschke 104!

*Office Hours:* Mon., Wed., 2:30-3:50 p.m.; Tues., Thurs., 1:30-3 p.m.; Fri., 2:30-3:30 p.m.; and by appointment. (These are subject to change because I haven't scheduled a TBA course yet.) I teach another course MWF, 1-2:20 p.m., and I often have meetings at noon and at 4 p.m. Otherwise, I probably am in my office or elsewhere in Hentschke Hall; call first to make sure.

*Text: *The text,* Linear Algebra with Applications *(second edition), by Gareth Williams, is not yet available at the U of R Bookstore. Copies of the first few chapters, along with copies of *MATLAB Primer* (second edition), by Kermit Sigmon, will be distributed in class.

*Course Objectives:*

- To understand several important concepts in linear algebra, including systems of linear equations and their solutions; matrices and their properties; determinants and their properties; vector spaces; linear independence of vectors; subspaces, bases, and dimension of vector spaces; inner product spaces; linear transformations; and eigenvalues and eigenvectors;

- to apply these concepts to such real world phenomena as electrical networks, traffic flow, archeological dating, economic interdependencies, population movement, communication networks, and weather prediction;

- to learn to use the computer package MATLAB to perform matrix computations and to explore and analyze linear algebra concepts;

- to learn to prove mathematical theorems;

- to improve your ability to think logically, analytically, and abstractly; and

- to improve your ability to communicate mathematics, both orally and in writing.

*Grading: *

Attendance: 50 points

Daily homework: 150 points

Team projects: 100 points

Three exams: 100 points each

Final exam: 200 points

Total: 800 points

Earning 55% of the total points possible guarantees the student a grade of at least 0.7, earning 67% of the points at least a 1.7, earning 79% of the points at least 2.7, and earning 90% of the points at least 3.7.

*
Attendance:* During class sessions, we will explore and discuss linear algebra concepts and their applications. Because I believe these activities and discussions will be vital to your understanding of the course material, part of your grade will be based on your

You may discuss strategies for solving homework exercises with me, with tutors and with your classmates, and you should check answers to computational exercises with your classmates. However, unless I say otherwise, the work you hand in must be essentially your own. A good way to ensure this is to write up your solutions independently.

*Team projects:* Approximately once per week, in place of the daily homework assignment described above, there will be a *team project, *which you will complete with a partner or partners. In completing these assignments, you and your partner(s) are expected to contribute equally to the work you hand in or present. Some of the projects will require oral presentations; some will require written reports. These assignments generally will be started in class, but will be completed outside of class.

*Examinations:* There will be three examinations during the semester, on March 2, April 2, and May 6 (approximately). In addition, there will be a comprehensive final examination on [].

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Assignments for First Week of Class

*
Thursday, Feb. 4
* Read: Section 1.1, Systems of Two Linear Equations in Two Variables