Math 413/513 - Linear Algebra I
Dr. Radu C. Cascaval

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Syllabus

Homework

Exams

Lecture Notes

BlackBoard

Course Info:

Time/Place: Monday & Wednesday, 4:30-5:45pm, SENG B211
Office Hours: Monday and Wednesday 1:00-2:30pm or by appointment (ENG 271)
Course Website: http://www.uccs.edu/rcascava/Math413
Email: radu@uccs.edu

Course Description

The lectures will cover most sections in the book with the exceptions of Chapters 3 & 4.Topics that will be discussed include abstract vector spaces, linear independence, bases, linear transformations, eigenvalues and eigenvectors, inner product spaces, orthogonality, the Gram-Schmidt process, adjoint operators and Jordan canonical forms. The course has a BlackBoard companion website for access to grades throughout the semester, links to handouts, solutions to HMW exercises etc.

Students enrolled in this class must have already taken Math 313 (Intro to Linear Algebra) or equivalent, preferably within the past two years. Therefore, they are expected to be familiar with basic concepts (such as matrices, determinants, systems of linear equations) and have developed certain level of intuition of working with them. The majority of Chapters 3 & 4 will be the responsability of students to review (being similar to the Math 313 material). The present course will emphasize logical reasoning, operation with more abstract notions and proof techniques. Understanding and creative interpretation of the concepts will be expected rather than mere memorization of the facts. Successful students not only will gain better understanding of linear algebra, but also will improve their problem solving, abstraction and generalization skills. They will learn ways to clearly communicate mathematical ideas both verbally and in writing, and to build an organized context for the mathematics they learn.

Textbook (required):

Linear Algebra, 4th edition, S. Friedberg, A. Insel, L. Spence, Prentice Hall, 2003

Homework:

Bi-weekly sets of homework problems from the textbook and other sources will be assigned, with due date on Wednesdays, unless otherwise specified. No late homework will be accepted or graded. For Math 513 credit, students will have additional homework problems to turn in. Although I encourage discussions outside of classroom on the topics covered in class and on exercises in the book, group work on the HMW itself is discouraged AND individual solutions to homework problems are expected from each student.

Exams:

There will be 2 midterm Exams during the semester and a comprehensive Final Exam, as follows

Exam 1: Wednesday, Oct 6
Exam 2: Monday, Nov 15
Final Exam: Wednesday, Dec 15, 4:30-7:00pm due Thursday, Dec 16, before 5pm, (return to my office ENG 271)

There will be no make up exams so please mark your calendars! If a student informs me well before the exam date about absolutely having to miss an upcoming exam AND provides acceptable written verification in support of the request, then the final exam score will be used to replace that particular exam. If any of the above conditions is not satisfied, the student will get a zero on the missed exam. The above procedure may only be applied once. The Final Exam cannot be missed under any circumstances.

Grading:

The course grade will be the higher of the two derived according to the following schemes: Scheme 1 = homework (30%), the two exams (20% each) and the final exam (30%); Scheme II = homework (30%), the best of two exams (30%) and final (40%). The final scores will be 'curved' to reflect the class distribution. Each student will receive a letter grade based on his/her relative standing in the class. Although attendance and participation do not formally enter the above computation, they will be taken into account every time one's score falls close to the cut-off value for a particular letter grade. At the same time you may be assured that if your score is at least 90% (or 80%,70%), then your letter grade will be at least A (or B, C respectively).

Other policies:

To make the most of your class, you are required to attend every class session. Students should notify (in advance) the instructor if they need to miss more than one session. Supporting documentation may be required. Drop dates: Please seek counseling from the Dean's office before dropping any course and note the following important dates: Sept 9 – last day to drop and receive a full tuition refund; Oct 29 – last day to drop without special permission from the Dean.

Academic Dishonesty:

Academic honesty is fundamental to the activities and principles of a university. All members of the academic community must be confident that each person's work has been responsibly and honorably acquired, developed, and presented. Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful. The academic community regards academic dishonesty as an extremely serious matter, with serious consequences that range from probation to expulsion. When in doubt about plagiarism, paraphrasing, quoting, or collaboration, consult the course instructor.

Disability Services:

Students with disabilities should contact the Office of Disability Services (Main Hall 105, 255-3354) and also notify the instructor of any special needs. They should provide a letter of certification from the Office of Disability Services within the first 2 weeks of classes.

Tentative Schedule for Fall 2010: (Check website for updated version)

		Lecture 1		Mon 8/23		Introduction. Vector Spaces
		Lecture 2		Wed 8/25		Subspaces
		Lecture 3		Mon 8/30		Linear Combinations. Linear Systems
		Lecture 4		Wed 9/1		Linear Dependence and Independence
		Lecture 5		Wed 9/8		Bases and Dimension
		Lecture 6		Mon 9/13		Replacement Theorem
		Lecture 7		Wed 9/15		Linear Transformations
		Lecture 8		Mon 9/20		Matrix Representation of Linear Transformations
		Lecture 9		Wed 9/22		Composition of Linear Transformations
		Lecture 10		Mon 9/27		Invertible Transformations and Isomorphisms
		Lecture 11		Wed 9/29		Change of Bases
		Lecture 12		Mon 10/4		Rank of a Matrix and Matrix Inverses
				Wed 10/6		Exam 1
		Lecture 13		Mon 10/11		Applications of Rank and Nullity
		Lecture 14		Wed 10/13		Eigenvalues and Eigenvectors
		Lecture 15		Mon 10/18		Diagonalizability
		Lecture 16		Wed 10/20		Algebraic and Geometric Multiplicity
		Lecture 17		Mon 10/25		Invariant Subspaces and Cayley-Hamilton Theorem
		Lecture 18		Wed 10/27		Inner Product Spaces
		Lecture 19		Mon 11/1		Gram-Schimdt Orthogonalization
		Lecture 20		Wed 11/3		Orthogonal Complement. Orthogonal Projection
		Lecture 21		Mon 11/8		Adjoint of a Linear Transformation. Dual Spaces
		Lecture 22		Wed 11/10		Normal and Self-Adjoint Operators
				Mon 11/15		Exam 2
		Lecture 23		Wed 11/17		Unitary and Ortogonal Operators
		Lecture 24		Mon 11/22		Orthogonal Projections. Spectral Theorem
		Lecture 25		Mon 11/29		Singular Value Decomposition and Other Applications
		Lecture 26		Wed 12/1		Jordan Canonical Forms I
		Lecture 27		Mon 12/6		Jordan Canonical Forms II
		Lecture 28		Wed 12/8		Minimal Polynomial
				Wed 12/15		Final Exam