Math 5330/6330 - REAL Analysis - Spring 2018
Dr. Radu C. Cascaval

HMW 3: Due Wed, Feb 14

Sect 3.1 #3, 9; Sect 3.2 # 16, 18, 22; Sect 3.3 # 31

HMW 2: Due Wed, Jan 31

Sect 2.4: #17, 20, 21, Sect 2.5: 24, 26, 28

HMW 1: Due Wed, Jan 24

Sect 2.1 # 1,3; Sect 2.2 # 6,7,9; Sect 2.3 # 14, 15

Course Info:

Time: Mon & Wed 1:40 - 2:55 pm (Jan 17 - May 10) 
Place: OSB B213
Office Hours: Mon & Wed 10:00-11:00 am or by appointment
Website: http://academics.uccs.edu/rcascava/Math5330

Course Description:

Lebesgue measure, measurable and nonmeasurable sets, sigma algebras. Lebesgue integral, comparison with Riemann integration, Monotone and Dominated Convergence Theorems, Fatou’s Lemma. Differentiation, functions of bounded variation, absolute continuity integration in product spaces, Fubini’s Theorem. Prer., MATH 4320/5320 - Modern Analysis II

Textbook (required):

Real Analysis, by H.L. Royden & P.M. Fitzpatrick: 4th edition, Pearson 2010

Grading:

The grade will consist of weekly HMW (30%), a midterm exam (30%) and the final exam (40%). For Math 6330 credit, students will be expected to complete a written report on an advanced topic related to the material covered in class, and make a short presentation toward the end of the semester, which will count as 20% part of the final exam grade. For Math 5330 this scheme is available as an option too.

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: Jan 31, 2018 – last day to drop and receive a full tuition refund; March 30, 2018 – last day to drop without special permission from the Dean. Pleaase note: Full semester length courses may be dropped until 11:50pm on Wednesday, January 31 in your MyUCCS Portal. All Course Change Forms (Add/Drop Forms) must be turned into the Office of the Registrar (Main Hall 108) by 5:00pm on Wednesday, January 31. Full semester-length courses dropped on an individual basis within myUCCS Portal after January 31 will receive an official grade of W and DO NOT receive a refund. You may drop full semester length spring courses in your myUCCS Portal until Friday, March 30 at 11:50pm and receive a grade of 'W'.  To withdraw from courses after Friday, March 30, you must obtain instructor and dean approval.  Forms can be requested in the Office of the Registrar - Main Hall 108.

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.