Summer 2019 - University of Houston

# Summer 2019

 Course Section Course Title & Session Course Day & Time Rm # Instructor Math 4377 - 01 11151 Advanced Linear Algebra I (Session #2: 06/03—07/03) MTWThF, 10am—Noon SEC 105 A. Haynes Math 4378 - 01 12367 Advanced Linear Algebra II (Session #4:07/08—08/07) MTWThF, 10am—Noon F 162 A. Török Math 4389 - 03 16578 Survey of Undergraduate Math (Session #4: 07/08—08/07) MTWThF, 10am—Noon SEC 203 D. Blecher

 Course Section Course Title Course Day & Time Instructor Math 5310 16560 History of Mathematics (Session #4: 07/08—08/07) (online) S. Ji Math 5336 11662 Discrete Mathematics (Session #2: 06/03—07/03) (online) K. Kaiser Math 5341 17811 Mathematical Modeling (Session #4: 07/08—08/07) (online) J. Morgan Math 5382 14092 Probability (Regular Session: 06/03—07/24) (online) J. West Math 5389 14463 Survey of Mathematics (Session #2: 06/03—07/03) (online) G. Etgen

 Course Section Course Title Course Day & Time Rm # Instructor TBD TBD (TBD) TBD, TBD TBD TBA

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 Math 4377 - Advanced Linear Algebra I Prerequisites: Text(s): Linear Algebra, Fourth Edition by  Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence Description: Syllabus:  Chapter 1, Chapter 2, Chapter 3, Chapter 4 (4.1-4.4), Chapter 5 (5.1-5.2) (probably not covered) Course Description: The general theory of Vector Spaces and Linear Transformations will be developed in an axiomatic fashion. Determinants will be covered  to study eigenvalues, eigenvectors and diagonalization. Grading:  There will be  three  Tests and the Final. I will take the two highest test scores (60%) and the mandatory final (40%). Tests and the Final are based on homework problems and material covered in class.

 Math 4378 - Advanced Linear Algebra II Prerequisites: Math 4377 or Math 6308 Text(s): Linear Algebra, 4th edition, by Friedberg, Insel, and Spence, ISBN 0-13-008451-4 Description: The instructor will cover Sections 5-7 of the textbook. Topics include: Eigenvalues/Eigenvectors, Cayley-Hamilton Theorem, Inner Products and Norms, Adjoints of Linear Operators, Normal and Self-Adjoint Operators, Orthogonal and Unitary Operators, Jordan Canonical Form, Minimal Polynomials.

 Math 4389 - Survey of Undergraduate Math Prerequisites: MATH 3330, MATH 3331, MATH 3333, and three hours of 4000-level Mathematics. Text(s): Instructors notes Description: A review of some of the most important topics in the undergraduate mathematics curriculum.

 MATH 5310 - History of Mathematics Prerequisites: Graduate standing Text(s): No textbook is required. Description: This course is designed to provide a college-level experience in history of mathematics. Students will understand some critical historical mathematics events, such as creation of classical Greek mathematics, and development of calculus; recognize notable mathematicians and the impact of their discoveries, such as Fermat, Descartes, Newton and Leibniz, Euler and Gauss; understand the development of certain mathematical topics, such as Pythagoras theorem, the real number theory and calculus. Aims of the course: To help students to understand the history of mathematics; to attain an orientation in the history and philosophy of mathematics; to gain an appreciation for our ancestor's effort and great contribution; to gain an appreciation for the current state of mathematics; to obtain inspiration for mathematical education, and to obtain inspiration for further development of mathematics. On-line course is taught through Blackboard Learn, visit http://www.uh.edu/webct/ for information on obtaining ID and password. The course will be based on my notes. Homework and Essays assignement are posted in Blackboard Learn. There are four submissions for homework and essays and each of them covers 10 lecture notes. The dates of submission will be announced. All homework and essays, handwriting or typed, should be turned into PDF files and be submitted through Blackboard Learn. Late homework is not acceptable. There is one final exam in multiple choice. Grading: 40% homework, 45% projects, 15 % Final exam

 MATH 5336 - Discrete Mathematics Prerequisites: Graduate standing Text(s): Discrete Mathematics and Its Applications, Kenneth H. Rosen, seventh edition, McGraw Hill, ISBN-13 978-0-07-288008-3, ISBN-10 0-07-288008-2. Instructor lecture note: Plus: on the Zermelo-Fraenkel Axioms and Equivalence of Sets. Description: Syllabus: Chapter 1 (Logic and Proofs): 1.1, 1.3, 1.4 -1.6  , Chapter 2 (Sets and Functions), Chapter 5 (Induction): 5.1-5.3, Chapter 9 (Relations) The Zermelo Fraenkel Axioms; Equivalence of Sets in form of  my notes. Grading: Midterm is worth  40%, the final is worth 40% and Homework is worth 20%. For turning in Homework, students need to get the software program Scientific Notebook.

 MATH 5341- Mathematical Modeling Prerequisites: Graduate standing. Three semesters of calculus or consent of instructor. Text(s): TBD Description: Course Topics: Basics of multivariable calculus and linear algebra Orthogonality, projection and visualization in higher dimensions Least squares approximation and multiple linear regression Stability theory associated with steady states and periodic solutions for continuous dynamical systems (systems of ODEs) Stability theory associated with steady states and periodic solutions for discrete dynamical systems Multiple applications Software: Students can use anything they want. I'll provide guidance and sample code using Excel, Matlab and Python. The syllabus is available at this link.