Class meets Tuesday & Thursday in Room MS 118 from 2:20 – 3:45pm

Instructor:

Toni Parsons

Office:

MS 215N

Phone: 619-388-2394

E-mail Address: [email protected] I check my voice mail only once a day, but I check my e-mail all day long (Monday through Friday). The best way to get a hold of me is by e-mail. Please put Math 254 in the subject box. If you are going to be absent, simply send me an e-mail letting me know. I do not respond to e-mails unless you ask for a response.

Office Hours:

M – Th 11:30 – 12:30, and F – by appointment

Description of Course:

This course serves as an introduction to the theory and applications of elementary linear algebra, and is the basis for most upper division courses in mathematics. The topics covered in this course include matrix algebra, Gaussian Elimination, systems of equations, determinants, Euclidean and general vector spaces, linear transformations, orthogonality and inner product spaces, bases of vector spaces, the Change of Basis Theorem, eigenvalues, eigenvectors, the rank and nullity of matrices and introduction to linear transformations. This course is intended for the transfer student planning to major in mathematics, physics, engineering, computer science, operational research, economics, or other sciences.

Prerequisites:

MATH 151 with a grade of "C" or better, or equivalent.

Course Objectives:

Upon successful completion of the course the student will

be able to:   

Solve systems of linear equations using several algebraic methods. Construct and apply special matrices, such as symmetric, skew-symmetric, diagonal, upper triangular or lower triangular matrices. Apply all the algebraic matrix operations, including multiplication of matrices, transposes, and traces.

 

               

Calculate the inverse of a matrix using various methods, and perform application problems involving the inverse. Compute the determinant of square matrices and use the determinant to assess invertibility. Derive and apply algebraic properties of determinants. Perform vector operations on vectors from Euclidean Vector Spaces including vectors from R^n. Compute the equations of lines and planes and express them in vector form. Perform linear transformations in Euclidean vector spaces, including basic linear operators, and determine the standard matrix of the linear transformation. Derive whether a given structure is a vector space and identify whether a given subset of a vector space is itself a vector space. Analyze whether a set of vectors spans a space, and if such a set is linearly dependent or independent. Assess if a set of functions is linearly independent using various techniques including calculating the determinant of the Wronskian. Solve for the basis and the dimension of a vector space. Determine the rank, the nullity, the column space and the row space of a matrix. Identify orthogonality between vectors in an abstract vector space by means of an inner product, and compute the inner product between vectors of any inner product space. Calculate the QR-decomposition of a matrix using the Gram-Schmidt process. Express a vector space via change of base, including computation of the transition matrix and determining an orthonormal basis for the space. Compute all the eigenvalues of a square matrix, including any complex eigenvalues, and determine their corresponding eigenvectors. Assess if a square matrix is diagonalizable and derive the diagonalization of a matrix whose eigenvalues are easily calculated. Apply linear transformations among abstract general vector spaces, and derive the rank, the nullity and the associated matrix of the transformation. Prove basic results in linear algebra using appropriate proof-writing techniques such as linear independence of vectors; properties of subspaces; linearity, injectivity and surjectivity of functions; and properties of eigenvectors and eigenvalues.

Student Learning Outcomes:   

A successful student will:

find the basis for the kernel of a linear transformation for a given matrix. be able to orthogonally diagonalize a 3x3 symmetric matrix. be able to find bases for the three fundamental subspaces of a matrix (rowspace, colspace, and nullspace).

Text and Materials:   

Elementary Linear Algebra by Larson, Edwards, and Falvo (8th edition). (You can get the ebook or rent the book from www.cengagebrain.com.) You will also need a scientific calculator, but a graphing calculator will be much more useful. You will also need access to the Blackboard website for this class.

Homework:

Homework will not technically be assigned. Instead you will have weekly homework quizzes that will contain problems from the book. It is strongly recommended that you try at least some of the odd problems in the book (or see the suggested problems on the website). I will answer a few questions at the beginning of class based on the material covered in the previous class. You can always come to my office hours if you have further questions. The homework quizzes will be due as scheduled and will be handed out a week ahead. There will be 13 of these quizzes and the lowest quiz will be dropped. Every late quiz will receive 3 points off, and no quizzes will be accepted after the answer key is posted on Blackboard.

Evaluation: 

Thirteen quizzes worth 25 points each. Lowest quiz will be dropped. (300 points)



Three tests worth 50 points each. (150 points) o No test will be dropped, but your grade on the final will replace your lowest test grade, if applicable.



Comprehensive final exam given on the last day (May 25th). (100 points) This gives a total of 550 points. 495 – 550 A 440 – 494 B 385 – 439 C 330 – 384 D

Attendance Requirements:

It is the student’s responsibility to add, drop, or withdraw from classes before the appropriate deadlines. If you decide to withdraw from this course, please let me know as a courtesy. If you fail to withdraw before the deadline, and you stop coming to class, a final grade must be assigned to you. Regular class attendance is a requirement for this class. You are responsible for all material covered in class during your absence. You are allowed 3 unexcused absences. I have the right to drop you after the 4th absence before the withdrawal deadline. It is possible to re-enroll before the withdrawal deadline if you can convince me of your motivation to stay. If you are a student receiving federal aid, I am required by law to drop you and report your last date of academic attendance within 22 days. You will be required to pay back any monies that you collected during the time that you were not attending class. Being late to class one or two times during the semester is understandable. However, habitual tardiness is strongly discouraged, for it is both discourteous and disruptive to class procedures. Habitual tardiness will be sufficient cause for exclusion from the class. If you must be late, enter the room quietly and take a seat.

Behavior:

Students are expected to respect and obey standards of student conduct while in class and on the campus. The student Code of Conduct, disciplinary procedure, and student due process can be found in the current college catalog under Policy 3100. If you violate Policy 3100, I have the right to ask you to leave the class for two days. You will not be able to make up any work that is missed in those two days. If you refuse to leave, I have the right to request a police escort. You will be asked to leave the class if you exhibit deliberate behavior which prohibits or impedes any member of the class from any class assignment objective or learning opportunity within the classroom. You will not be allowed to leave the room once a test has started. Please make sure you have taken care of all necessary business prior to the start of the exam. Please turn off cell phones and put them away. I would rather just not see them. If communicating with someone outside of class or playing games is more important than learning, then politely leave the classroom.

Cheating (copying) will not be tolerated under any circumstances. If a student is caught cheating on a quiz or test, he/she will receive a zero and that grade cannot be dropped. Quizzes are take-home. Collaboration is encouraged, but please turn in your own work. Keep your eyes on your own paper during a test. Cheating on the final will result in an automatic F in the class. The goal of the Mathematics Department at Mesa College is to provide all students the opportunity for a safe, fair, and effective learning environment. The instructors are dedicated professionals who facilitate your learning in a student-focused classroom by setting high expectations while providing multiple avenues for learning. Students are expected to respect teachers, other students and themselves in order to enhance a positive and successful learning experience.

Academic Accommodation:

Any student who may need an academic accommodation should discuss the situation with me during the first week.

Important Dates:  

02/10 Deadline to add with an add code. Deadline to drop with no “W” on record. 04/14 Withdrawal Deadline.

Tentative Schedule

Math 254 (44706)

Tuesday

Thursday

1/31

Friday

2/2

Introduction, 1.1

2/3

1.2, 1.3

2/7

2/9

1.3, 2.1 2/16

2.4, 2.5

2/10 Last Day to Add

Q 2 due

2/17 Lincoln’s Day

Q 3 due

2/24

2.5, 3.1

2/21

2/23

3.2, 3.3 2/28

Q 1 due

2.2, 2.3

2/14

3.3, 3.5 Q 4 due

3/2

Review

3/3

Test 1 (1, 2, 3)

3/7

3/9

4.1, 4.2

3/10

4.2, 4.3

3/14

3/16

4.4, 4.5

Q 5 due

3/17

Q 6 due

3/24

4.5, 4.6

3/21

3/23

8.1 – 8.3

4.7, 4.8 3/28

3/30

Spring 4/4

Q 7 due

4/11

3/31

YEAH!!!!

Break 4/6

8.4, 5.1 4/13

4/18

Q 8 due

4/7

Q 9 due

4/14 Withdrawal Deadline

5.2, 5.3

5.5

Review 4/20

4/25

4/21

6.1, 6.2

Test 2 (4, 5, 8) 4/27

6.2, 6.3 5/2

5/4

5/9

4/28

Q 11 due

5/5

Q 12 due

5/12

7.1, 7.2 5/11

7.3, 8.5 5/16

Q 10 due

6.4

6.5

7.4 5/18

Review/Catch-up 5/23

Spring 2017

Q 13 due

Review for Final

5/19

Test 3 (6, 7) 5/25

5/26

Final (everything)