STAT H-309

Office Hours: ( WEDNESDAY 12pm to 1pm / or by appointment.) LAST TEAR

Office Hours for Theory Course: 17-18

Sunday: 1:00 PM - 2:00 PM

Tuesday: 11:00 AM - 12:00 PM

Wednesday: 2:00 PM - 3:00 PM

/ by appointment.

Stat H-309: Mathematical Analysis 3 credits

The real number system; axioms and completeness and its consequences; Dedekind cut, sets, compact sets; simple operation on them.

Sequence of functions of one and several variables; limit; continuity; continuous functions; uniform continuity; differentiation and integration; Infinite series of constants and functions; convergence and divergence; Power series: differentiation and integration of power series; Taylor expansion (with remainder or in infinite series).

Metric and topological spaces; limit points; open and closed sets; interior and exterior points; boundary points; Continuous mapping and Cauchy sequences.

Measure and integrals on abstract sets on real lines; Cramer measurability: fundamental definitions; auxiliary lemma; fundamental theorems; Measurable functions; Lebesgue measure on a real line, plane; Integrals; Riemann-Steiljes integrals. Distinction between probability measure and Lebesque measure and Lebesque integrals.

Mã ứng dụng trong Statistics.

Text:

1. Rudin, W. (1976). Principles of Mathematical Analysis. McGraw-Hill.

2. Bartle, RG, & Sherbert, DR (2000). Introduction to real analysis. Fourth Edition. New York, John Wiley & Sons.

3. Simmons, GF ,, Introduction to Topology & Modern Analysis, McGraw-Hill, NY

4. Berherion SK, Introduction to Measure & Integration.

References:

1. Royden, HL, Real Analysis, Mcmillan, NY

2. Schaum Series, Advanced Calculus & Real Analysis.

3. Sipschute, S., General Topol; ogy, McGraw-Hill, NY

4. Halmos, PR, Measure Theory, Van Nostrand, NY

5. Billingeley, P., Probabability and Measure, Wiley, NY

6. Kingman, JFG, Measure and Probability, CUP.

7. Pitt, HR, Integration and Probability measure, Oliver and Boyed.

8. William, FT (2011): I ntroduction to Real Analysis, Peason Publication, USA.

Results of assignments and tests

(please report any errors to hkdas_math@du.ac.bd

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Total # of Student present in the exam

Note: If you have any question about Midtertm and attendance Marks please talk to me before October 31, 2017, Wednesday, 11 AM-4amPM.