MATH 250: ADVANCED
CALCULUS IN STATISTICS
Instructor: Baver OKUTMUSTUR
Schedule: Lectures: Tuesday 08:40-10:30 (YP-A3), Thursday 15:40-17:30 (YP-A3); Recitations: Friday 8:40-10:30 (YP-A2)
Office Hours : M242 Tuesday 12:30-13:30
Course Assistant: Muhammed Erkam ÖZDEMiR.
His office hours: ...
Note: Please follow announcements and updates about the course via Metu.class
Content:
1. An Introduction to Set Theory, Linear Structure and Topology of Euclidean Spaces.
2. Infinite Sequences and Series of Functions.
3. Multidimensional Calculus. Functions of Several Variables, Limit, Continuity, Derivatives, Taylors Theorem.
4. Inverse and Implicit Function Theorems, Optimization, Lagrange Multiplier Methods for Multivariable Functions
5. Functions of Bounded Variation, Riemann-Stieltjes Sum and Riemann-Stieltjes Integral
6. Bounded Convergence, Riesz Representation Theorems and Applications in Statistics (if time permits).
Goals:
The objective of this course is 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:
Midterm I (25%) (31.03.2026)
Midterm II (25%) (12.05.2026)
Final (40%) (TBA)
Quiz (10%)
Make up Exams:
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. There will be one make-up examination after the final exam
and all topics will be covered in this exam.
NA Criteria:
Before the final exam, students will be categorized in the following way:
1) M1 + M2 >= 20
2) M1 + M2 < 20,
for which M1 is the Midterm 1 score out of 100, and M2 is the Midterm 2 score
out of 100.
- Students in group 1 will be able to take the final exam.
- Students in group 2 will NOT be able to take the final exam. They will get an
automatic NA grade.