BCU Department of Mathematics

Professor Dennis Clayton

Mary McLeod Bethune picture locket.

MA 335 A Course Outline

Prerequisites

MA 241 with a 'C' or better final grade or instructor consent (this means you will need a course override form signed by Dr. Clayton). No exceptions.

You may be dropped from the class at any time during the semester if you have not met these prerequisites.

Course Description in the BCU Catalog

Prerequisite MA 242. Uses of vectors and matrices in coordinate geometry, concept of linear independencies, finite dimensional vector spaces, sub-spaces, basis, dimension; linear equations, use of matrices and determinants in the solution of linear equations; matrix operations; vector fields, and linear combinations; quadratic forms.

Textbook(s) and Required Materials

Linear Algebra, 2nd ed, David Poole, Thompson Brooks/Cole, 2006. ISBN: 0-534-99845-3

Buy a computer if you do not already own one.

Main Course Goals

1. The student will develop and use methods of solving systems of linear equations.
2. The student will develop, memorize, and use the basic mathematical concepts of vector spaces.
3. The student will continue to develop their grasp of mathematical abstraction and the logic of mathematical proof (you only improve, you never finish).

Impact

Impact on BCU Mission and Institutional Student Learning Outcomes (ISLOs) - Through the attainment of the course student learning objectives (CSLOs), students will acquire knowledge, skills and competencies outlined in the Institutional Student Learning Outcomes, School Student Learning Outcomes (SSLOs) and Program Student Learning Outcomes (PSLOs) . The Course Student Learning Objectives fully support the University Mission and Core Values as stated in the Strategic Plan; as well as, the School Goals.

Program Student Learning Outcomes (PSLOs) addressed in Course Learning Objectives.

• PSLO 5 - Proficiency in essential fields: Abstract Algebra
• PSLO 6 - Proficiency in essential fields: Computational Mathematics
• PSLO 9 - Ability to read and construct mathematical proofs
• PSLO 10: Ability to reason in abstract mathematical systems and models
• PSLO 11 - Ability to read new mathematics and formulate mathematical models and arguments
• PSLO 12. Students will apply STEM knowledge, skills and methods to address real world problems.
  

Course Student Learning Objectives

A student completing this course with a C or better...

1. By the end of the topic on systems of linear equations, will be able to (PSLO 5, 6, 9)
   1. Solve systems of linear equations by using the method of Gaussian elimination and Gauss-Jordan elimination.
   2. Know the properties of systems of homogeneous linear equations.
   3. Perform algebra on matrices and determinants.        
   4. Find inverses of certain matrices.
   5. Express a matrix in abstract form and locate any specific element of a matrix.
   6. Add, subtract, multiply and divide matrices.
2. By the end of the topic on determinants, will be able to (PSLO 5, 6, 9)
   1. Evaluate a determinant by the row reduction.
   2. Explain the properties of determinants.
   3. Apply Cramer's rule to determinants.
3. By the end of the topic on two and three-space vectors, will be able to (PSLO 5, 6, 9)
   1. Graph vectors in 3-space.
   2. Graph a plane in 3-space.
   3. Compute the norm of a vector.
   4. Find the inner product of vectors.
   5. Find the cross product of vectors.
4. By the end of the topic on general vector spaces, will be able to  (PSLO 5, 6, 10, 11)
   1. Use the axioms of a vector space to show that a given set of objects is vector space.
   2. Determine the subspace of a vector space.
   3. Find scalars to show that a vector may be represented as a linear combination of other vectors.
   4. Find the basis for a given vector space.
   5. Show that you know the difference between linearly independence and linearly dependence when finding the smallest set that spans a space.
   6. Find the rank of a matrix.
   7. Find an inner product space on a vector space.
   8. Find an orthonormal basis for an inner product space.
   9. Use the Gram-Schmidt process to convert a basis to an orthonormal basis.
   10. Find the transition matrix from change of basis.
5. By the end of the topic on linear transformation, will be able to (PSLO 5, 6, 9)
   1. Find the linear transformation of a vector space V to a vector space W.
   2. Find the kernel and range of a linear transformation.
   3. Show that every linear transformation on a finite dimensional vector space can be regarded as a matrix transformation.
   4. Find similar matrices.
6. By the end of the topic on eigenvalues and eigenvectors, will be able to: (PSLO 5, 6)
   1. Find eigenvalues
   2. Find eigenvectors.
   3. Diagonalize a matrix.
   4. Show that an orthogonally diagonalizable matrix is symmetric

General Requirements

• Attendance is mandatory! All students are required to attend each class, to arrive on time, and to remain until the end. Attendance is considered essential for the student to obtain as much as possible from the lecture and the lab work done in class. The student is responsible for all notes, assignments,  announcements, and information given in class whether or not the student is present.  Lectures will not be repeated in class or in the professor's office. Each student is encouraged to find a colleague to contact in the event of an absence.
• Students will use standard English in class--written and spoken..
• Students will keep a notebook consisting of notes, assignments, etc., and will bring it to class daily.
• Students are expected to make thorough preparation for each class session. Students are encouraged to reread the notes and rework the examples from class.
• Students are expected to do all assignments--both in class assignments and homework--and to participate in class discussions.
• Students are encouraged and expected to do individual study assignments daily. After each class and before the next class meeting, each student is expected to spend at least 2 hours on assignments, homework, or studying the material from class.
• The subject line of email sent to me must start with: MA335 followed by your name. For instance, MA335 Bob Smith etc.
• Send me an email from the email account that you use daily.
• Plagiarism will not be tolerated. You must do your own work.
• Cheating will not be tolerated. You must do your own work.
• All essay work must be typed. Hand written work will not be accepted unless explicitly stated in the assignment. Never write on both sides of the paper.
• Late assignments will not be accepted because we will usually work the assigned problems in class on the day they are due.
• The Bethune-Cookman University dress code requires that you wear appropriate attire to class. You are not allowed to wear hats, caps, bandanas or do-rags in class. Pants are to be worn over your underwear. You will be asked to leave the class if your attire is inappropriate for a BCU student in a science class.
• You are an adult. Act like one:
  • Do not sleep in class. If you are so tired that you feel that you are going to fall asleep, then stand up. Everyone will laugh at you, but I will not ask you to leave and I will not penalize you for doing it. If you fall asleep during my lecture, I will be offended and will ask you to leave.
  • Do not walk out of class during the lecture. Show common courtesy. If you walk out often enough, it will affect your grade. I may mark you absent.
• See me immediately if you are having problems with this course.

Methods of Instruction

There are two lecture/discussion periods each week. We will discuss the material in the book and illustrate it with examples. You are expected to participate in the discussions. Be prepared to discuss the material.

Each Student will have in his/her possession a copy of the required textbook and a calculator.

All students are required to attend each class, to arrive on time, and to remain until the end.

After each class and before the next class meeting, each student is expected to spend at least 2 hours on assignments, homework, or studying the material from class.

You will have to work to pass this course. This is not an easy course. However, almost all of the problems previous students have had with this course resulted from falling behind--not reading the assigned material, not starting the homework when it was assigned, cramming for exams, and so on. If you fall behind, you will have a difficult time catching up. Study the reading assignments as soon as they are assigned, start on the homework immediately. If you put forth the effort, you will get an 'A' in the class.

You will be dropped from the course at midterm if you have four or more absences from the class. You are required to attend all the lectures. You are marked absent if you are not present when the roll is taken. If you are late, you can tell me at the end of the class period. Two lates equal one absent.

Missing a class is no excuse for not handing in an assignment or for not knowing about an assignment. Assignments will be posted on the assignments web page (not ready yet, ma??? assignments).

Class participation counts 10% of your grade. You cannot participate if you are absent.

Topical Outline

• Topical Outline and Lecture Schedule

• Assignments

Technology

All essays must be typed and formatted in the standard "term paper format". We will discuss the requirements, if necessary.

We will have several assignments using one (or more) of the commonly available mathematics programs to solve linear algebra problems. The following are recommended: Mathematica, Maple, and Derive (in order of decreasing cost).

Several assignments will involve Internet searching (on interesting mathematical topics) and to find graphical simulation programs.

Assessment/Evaluation/Grading scale

Class Participation (10% of your final grade).
You cannot participate if you are absent. This is my subjective evaluation of your preparation for classroom discussion and participation, attitude, attendance, and so on. Don't expect much if you sleep in class, constantly leave to answer your cell phone or pager, or otherwise behave in an unpleasant or unprofessional manner.

Exams (40% or your final grade).
All students enrolled in the class will take quizzes and examinations at the same time.

• Midterm Exams (100 points each)
  One-hour exams are called a midterms. There will be at least two, in-class midterms. These are closed book, closed notes exams. These are memory testing exams. There are no makeup exams, so do not cut class the day of an exam.
• Final Exam (200 points)
  The final exams will be given on the days and hours scheduled by the Registrar's Office for the class and the lab. I will post these as soon as they are announced. The final exam will be a two-hour in-class exam.

Homework and Quizzes (50% of your final grade).
All homework must be cleanly presented, neat, and clearly showing your work. Neatness counts! If I cannot read it, I cannot grade it. Do not write on both sides of the paper. Turn in the assignments with the problems in the assignment order. If your work is not in order, or is messy or otherwise unappealing, or hard to read, the grade will be lowered at least one letter grade and may not be graded at all. This also means you must turn in all the problems together in one package. Assignments are due at the beginning of class. We will usually work homework problems in class the day the assignment is due. Late assignments will not be accepted. To do so would be unfair to everyone who worked on the problems before seeing how to do them in class .

How to hand in your homework: Hand in the assignments at the beginning of class on the due date. Remember, late assignments will not be accepted, so do not skip class to work on an assignment.

Policy on copying (also known as cheating and plagiarism)
All assignments are individual assignments unless clearly labeled a group assignment. Do not work together on individual assignments. Working in a group frequently means that one person does all the work and also all the learning. You will have to work by yourself on the tests, so be prepared.

If your homework looks too much like another student's homework, then I will assume one (or more) of you copied. You will all get either a zero for the homework, or, if I am in a good mood, which is unlikely, I will divide the grade evenly among those in the group.

Policy on extra work
Do not ask for extra work unless you currently have an 'A' in the course. Extra work is in addition to the assignments, not a replacement for them. There are no make-up assignments or projects or exams.

Do not bring a cell phone to an exam. If you do, and it is visible or audible, I will assume you are cheating and you will get a zero on the test.

This course observes the College's grading scale:

An F- (that's an F-minus) grade is reserved for work that was not turned in or was so poor that it should not have been turned in. Note that one F- requires four A's to average out to a passing grade of C:
      Average ( F- + A + A+ A + A ) = C
      Average ( 0 + 95 + 95 + 95 + 95 ) / 5 = 76     (only a C)

Midterm Grades
If you get a 'D' at midterm, you may interpret the grade as a red flag that you are not passing. However, if you put forth more effort, you should be able to pass the course. If you get an 'F' at midterm, you should take this as a warning that, in my opinion, you will not pass the course. You should drop the course while you can. Remember, I cannot drop you after midterms.

Bibliography (additional reading for the over-achiever)

Appleton-Century Mathematics Series, Linear Algebra with Applications Including

Linear Programming, Meredith Corporation, 1971.

Ayres, Frank Jr., Matrices, Linear Algebra, Schaum's Outline Series, 1968.

Shields, Paul C., Elementary Linear Algebra, Worth Co., 1968.

Tucker, Alan, Linear Algebra:  An Introduction to The Theory and Use of Vectors and Matrices, Macmillan Publishing Company, New York, New York, 1993.

Zelinsky, Daniel, A First  Course in Linear Algebra, Academic Press, 1968.

Poole, David, Linear Algebra – A Modern Introduction – Second Addition, Thomson-Brooks/Cole Publishing, 2006.

Herman, Pepe, Moore, King, Linear Algebra – Modules for Interactive Learning Using Maple 6 (by the Linear Algebra Modules Project {LAMP}), Addison Wesley Longman Publishing, 2001.

Strang, Gilbert, Linear Algebra and Its Applications – fourth edition, Thomson Learning, Inc., 2006.

Lay, David C., Linear Algebra and Its Applications – third edition update, Pearson Addison Wesley, 2006.

Fall Semester, 2008
Last update: Aug 18, 2008

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