M250 ADVANCED CALCULUS IN STATISTICS

MATH 250: ADVANCED CALCULUS IN STATISTICS
Instructor: BAVER OKUTMUSTUR

Schedule
Lectures: Tuesday 08:40-10:30 (G202), Thursday 15:40-17:30 (YP-A3);
Recitations: Friday 08:40-10:30 (YP-A2 )

Content:
1. An Introduction to Set Theory, Linear Structure and Topology of Euclidean Spaces (2-3 Weeks).
2. Infinite Sequences and Series of Functions (2-3 Weeks).
3. Multidimensional Calculus. Functions of Several Variables, Limit, Continuity, Derivatives, Taylors Theorem, Inverse and Implicit Function Theorems, Optimization, Lagrange Multiplier Methods for Multivariable Functions (4-5 Week).
4. Functions of Bounded Variation, Riemann-Stieltjes Sum and Riemann-Stieltjes Integral (2-3 Weeks).
5. Bounded Convergence, Riesz Representation Theorems and Applications in Statistics (if time permits).

Goals:
The objective of this course is to familiarize the student with the conceptual as well as computational aspects of derivatives and integrals of functions of several variables,
sequences and series of functions and more advanced topics like Riemann-Stieltjes Integral, Bounded Convergence and Riesz Representation Theorems.

Text Book(s) and references:
1. Advanced Calculus, An Introduction to Linear Analysis by Leonard F. Richardson, Wiley, 2008.
2. Advanced Calculus with Applications in Statistics by Andre I. Khuri, Wiley Series in Probability and Statistics, 2003.
3. Advanced Calculus, W. Kaplan, 1993, Fourth Edition.
4. Advanced Calculus, M. Spiegel, 1962.

Exams and Grading:
1st Midterm (15%) (27.April.2023 at 15:40)
2nd Midterm (15%) (25.May.2023 at 15:40)
Final (60%) (TBA)
Quiz (15%)

Make up Exams:
-Make-up exam is for students who missed the midterm or the final exam due to an officially proven reason.
-There is NO make up exam for quizes.
-All announcements and paperworks are done after the final exam and all topics will be covered in this exam.
-Students who are eliminated by NA criterium cannot take this exam.
-In order to be eligible for entering a make-up examination for a missed examination, a student should have a documented or verifiable, and officially acceptable excuse.

Final Exam Entrance Conditions and NA Criteria:
To take the final exam, you need to

(*) take at least 20 over 200 from the sum of midterm exams (over 200). If you take MakeUp Exam from one of the Midterms, your grade from the other Midterm should be at least 10 (over 100)

A student who doesn't satisfy (*) receives the grade NA.