# Math 2318: Linear Algebra

### Spring 2018

Synonym: 30932, Section: 001, Northridge 2244
Monday / Wednesday 6:00 pm- 7:20 pm

Linear Algebra, MATH 2318, Learning Outcomes

Upon successful completion of this course, students will:

1.         Solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion.

2.         Carry out matrix operations, including inverses and determinants.

3.         Demonstrate understanding of the concepts of vector space and subspace.

4.         Demonstrate understanding of linear independence, span, and basis.

5.         Determine eigenvalues and eigenvectors and solve eigenvalue problems.

6.         Apply principles of matrix algebra to linear transformations.

7.         Demonstrate understanding of inner products and associated norms.

Course Objectives

The course objectives of Linear Algebra are:

1.      To use mathematically correct language and notation for Linear Algebra.

2.      To become computational proficiency involving procedures in Linear Algebra.

3.      To understand the axiomatic structure of a modern mathematical subject and learn to construct simple proofs.

4.      To solve problems that apply Linear Algebra to Chemistry, Economics and Engineering.

The topics that will enable this course to meet its objectives are:

(i)             the basic arithmetic operations on vectors and matrices, including inversion and determinants, using technology where appropriate;

(ii)           solving systems of linear equations, using technology to facilitate row reduction;

(iii)          the basic terminology of linear algebra in Euclidean spaces, including linear independence, spanning, basis, rank, nullity, subspace, and linear transformation;

(iv)          the abstract notions of vector space and inner product space;

(v)           finding eigenvalues and eigenvectors of a matrix or a linear transformation, and using them to diagonalize a matrix;

(vi)          projections and orthogonality among Euclidean vectors, including the Gram-Schmidt orthonormalization process and orthogonal matrices;

(vii)        the common applications of Linear Algebra, possibly including Markov chains, areas and volumes, Cramer's rule, the adjoint, and the method of least squares;

(viii)       the nature of a modern mathematics course: how abstract definitions are motivated by concrete examples, how results follow from the axiomatic definitions and are specialized back to the concrete examples, and how applications are woven in throughout. This course will present various "characterization" theorems (eg. characterizing isomorphic finite-dimensional vector spaces by their dimension and characterizing invertible matrices by various criteria);

(ix)          basic proof and disproof techniques, including mathematical induction, verifying that axioms are satisfied, standard "uniqueness" proofs, proof by contradiction, and disproof by counterexample.

ACC College Policies

Statement on Scholastic Dishonesty - A student attending ACC assumes responsibility for conduct compatible with the mission of the college as an educational institution.  Students have the responsibility to submit coursework that is the result of their own thought, research, or self-expression.  Students must follow all instructions given by faculty or designated college representatives when taking examinations, placement assessments, tests, quizzes, and evaluations.  Actions constituting scholastic dishonesty include, but are not limited to, plagiarism, cheating, fabrication, collusion, and falsifying documents.    Penalties for scholastic dishonesty will depend upon the nature of the violation and may range from lowering a grade on one assignment to an “F” in the course and/or expulsion from the college.  See the Student Standards of Conduct and Disciplinary Process and other policies at http://www.austincc.edu/current/needtoknow

Student Rights and Responsibilities - Students at the college have the rights accorded by the U.S. Constitution to freedom of speech, peaceful assembly, petition, and association. These rights carry with them the responsibility to accord the same rights to others in the college community and not to interfere with or disrupt the educational process. Opportunity for students to examine and question pertinent data and assumptions of a given discipline, guided by the evidence of scholarly research, is appropriate in a learning environment. This concept is accompanied by an equally demanding concept of responsibility on the part of the student. As willing partners in learning, students must comply with college rules and procedures.

Statement on Students with Disabilities - Each ACC campus offers support services for students with documented disabilities. Students with disabilities who need classroom, academic or other accommodations must request them through Student Accessibility Services (SAS, formerly OSD).  Students are encouraged to request accommodations when they register for courses or at least three weeks before the start of the semester, otherwise the provision of accommodations may be delayed.

Students who have received approval for accommodations from SAS for this course must provide the instructor with the ‘Notice of Approved Accommodationsfrom SAS before accommodations will be provided.  Arrangements for academic accommodations can only be made after the instructor receives the ‘Notice of Approved Accommodationsfrom the student.

Students with approved accommodations are encouraged to submit the ‘Notice of Approved Accommodationsto the instructor at the beginning of the semester because a reasonable amount of time may be needed to prepare and arrange for the accommodations.  Additional information about Student Accessibility Services is available at  HYPERLINK "http://www.austincc.edu/support/osd/" http://www.austincc.edu/support/osd/

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Please note, you are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be dismissed from the days activity, may be withdrawn from the class, and/or barred from attending future activities.

You are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be immediately dismissed from the days activity, may be withdrawn from the class, and/or barred from attending future activities.

Use of ACC email - All College e-mail communication to students will be sent solely to the students ACCmail account, with the expectation that such communications will be read in a timely fashion. ACC will send important information and will notify you of any college related emergencies using this account.  Students should only expect to receive email communication from their instructor using this account.  Likewise, students should use their ACCmail account when communicating with instructors and staff.  Instructions for activating an ACCmail account can be found at http://www.austincc.edu/accmail/index.php.

Testing Center Policy - Under certain circumstances, an instructor may have students take an examination in a testing center.  Students using the Academic Testing Center must govern themselves according to the Student Guide for Use of ACC Testing Centers and should read the entire guide before going to take the exam.  To request an exam, one must have:

·    Course Abbreviation (e.g., ENGL)

·    Course Number (e.g.,1301)

·    Course Synonym (e.g., 10123)

·    Course Section (e.g., 005)

·    Instructor's Name

Do NOT bring cell phones to the Testing Center.  Having your cell phone in the testing room, regardless of whether it is on or off, will revoke your testing privileges for the remainder of the semester.  ACC Testing Center policies can be found at http://www.austincc.edu/testctr/

Student And Instructional Services - ACC strives to provide exemplary support to its students and offers a broad variety of opportunities and services.  Information on these services and support systems is available at:   http://www.austincc.edu/s4/ Links to many student services and other information can be found at: http://www.austincc.edu/current/ For help setting up your ACCeID, ACC Gmail, or ACC Blackboard, see a Learning Lab Technician at any ACC Learning Lab.

Concealed Handgun Policy - The Austin Community College District concealed handgun policy ensures compliance with Section 411.2031 of the Texas Government Code (also known as the Campus Carry Law), while maintaining ACC’s commitment to provide a safe environment for its students, faculty, staff, and visitors. Beginning August 1, 2017, individuals who are licensed to carry (LTC) may do so on campus premises except in locations and at activities prohibited by state or federal law, or the college’s concealed handgun policy. It is the responsibility of license holders to conceal their handguns at all times. Persons who see a handgun on campus are asked to contact the ACC Police Department by dialing 222 from a campus phone or 512-223-7999.Refer to the concealed handgun policy online at austincc.edu/campuscarry.

Course Outline and Approximate Calendar:
Please note:  schedule changes may occur during the semester.
Any changes will be announced in class.
This is a pretty optimistic schedule, so there is a good chance we may have to drop a section or two…

 Week Dates Sections Topics 1 1/15/18 Holiday - no class 1/17/18 1.1 Vectors 2 1/22/18 1.2 The dot product 1/24/18 1.3 Hyperplanes in Rn 3 1/29/18 1.4 Gaussian elimination 1/31/18 1.5 Theory of linear systems 4 2/5/18 1.6 Applications 2/7/18 2.1 Matrix operations Test 1 – Dates to be announced in class 5 2/12/18 2.2, 2.3 Linear transforms and inverse matrices 2/14/18 2.4 Elementary matrices 6 2/19/18 2.5, 3.1 The transpose and subspaces of Rn 2/21/18 3.2 The four fundamental subspaces 7 2/26/18 3.3 Linear independence and basis 2/28/18 3.4 Dimension and its consequences 8 3/5/18 3.4 Dimension and its consequences 3/7/18 3.6 Abstract vector spaces Test 2 – Dates to be announced in class SPRING BREAK:  3/12/18 - 3/18/18 9 3/19/18 4.1 Inconsistent systems and projection 3/21/18 4.2 Orthogonal bases 10 3/26/18 4.3 The matrix of a linear transform and the change of base formula 3/28/18 4.4 Linear transforms on abstract vector spaces 11 4/2/18 5.1 Properties of determinants 4/4/18 5.2 Cofactors and Cramer’s Rule 12 4/9/18 5.3 Signed area in R2 and signed volume in R3 4/11/18 6.1 The characteristic polynomial Test 3 – Dates to be announced in class 13 4/16/18 6.2 Diagonalizability 4/18/18 6.3 More applications 14 4/23/18 6.4 The spectral theorem 4/25/18 7.2 Computer graphics and geometry 15 4/30/18 7.3 Matrix exponentials and differential equations 5/2/18 Review 16 5/7/18 Final Exam, Part 1 5/9/18 Final Exam, Part 2

This webpage was created by Marcus McGuff.
It was last updated on January 8, 2018 .