Mikhail Ivanov
Math Learning Center:
222, 234
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Math 567 Modern Number Theory
Have taught Spring 2025
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Math/Stat 431 Introduction to Probability
Have taught Spring 2025, Fall 2024, Fall 2021
- 2021/ Syllabus
- 2021/ Midterm 1, Solutions
- 2021/ Midterm 2, Solutions
- 2021/ Final, Solutions
- 2024/ Content
- Lecture 1. Introduction and definition of probability space
- Lecture 2. Constructions of probability spaces
- Lecture 3. Counting and geometric distribution
- Lecture 4. Computing probability by decomposing
- Lecture 5. Inclusion-Exclusion and Random variables
- Lecture 6. Conditional Probability
- Lecture 7. Bayes' formula
- Lecture 8. Independence
- Lecture 9. Repeated Independent Trials
- Lecture 10. Hypergeometric distribution and constructions from independent random variables
- Lecture 11. Conditional Independence
- Lecture 12. Continuous distributions and p.d.f
- Lecture 13. Cumulative distribution function
- Lecture 14. Expectation I
- Lecture 15. Expectation II
- Lecture 16. Varience
- Lecture 17. Normal Distribution
- Lecture 18. CLT for binomial random variable
- Lecture 19. Law of large numbers and applications of CLT
- Lecture 20. Poisson approximation
- Lecture 21. Overview of Poisson process
- Lecture 22. Exponential distribution and Moment generating function
- Lecture 23. Moment generating function and distributions
- Lecture 25. Joint distribution of discrete random variables
- Lecture 26. Joint continuous distribution of random variables
- Lecture 27. Joint distribution and independence
- Lecture 28. Sum of independent random variables I
- Lecture 29. Sum of independent random variables II
- Lecture 30. Exchangibility
- Lecture 31. The Indicator method
- Lecture 32. Covariance and correlation I
- Lecture 33. Covariance and correlation II
- Lecture 34. Tail Probabilities and The Law of Large Numbers
- Lecture 35. Central Limit Theorem
- Lecture 36. Conditional distribution for discrete random variable I
- Lecture 37. Conditional distribution for discrete random variable II
- Lecture 38. Conditional distribution for continuous random variable
- Lecture 39. Conditional Expectation
- Lecture 40. Conditional Expectation
- Lecture 41. Final Overview.
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Small group tutoring for Math 222 "Calculus II"
- Math Learning Center
- Content of Fall 2024
- (Review) Derivatives, Integration, Trigonometric and Inverse Trigonometric Functions. Please come to our review sessions
- (7.1) Integration by Parts
- (7.2) Trigonometric Integrals
- (7.3) Trigonometric Substitutions
- (7.4) Integration of Rational Functions
- (7.8) Improper Integrals
- (9.1, 9.2) Modeling with Differential Equations, Direction Fields and Euler's Method
- (Review) Midterm 1. Please come to our review sessions
- (9.3) Separable Equations
- (9.5) Linear Equations
- (10.1, 10.2) Curves Defined by Parametric Equations, Calculus with Parametric Curves
- (10.3) Polar Coordinates
- (Review) Limits. Please come to our review sessions
- (11.1) Sequences
- (11.2) Series
- (11.3) The Integral Test and Estimates of Sums
- (11.4) The Comparison Tests
- (11.5) Alternating Series
- (Review) Midterm 2. Please come to our review sessions
- (11.6) Absolute Convergence and the Ratio and Root Tests
- (11.8) Power Series
- (11.9) Representations of Functions as Power Series
- (11.10) Taylor and Maclaurin Series
- (12.1, 12.2) Three-Dimensional Coordinate Systems, Vectors
- (12.3) The Dot Product
- (12.4) The Cross Product
- (12.5) Equations of Lines and Planes
- (Review) Final Exam. Please come to our review sessions
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Math/Comp Sci 240: Introduction to Discrete Mathematics
Have taught Spring 2024
- 2024/ Syllabus
- 2024/ Midterm 1, Solutions
- 2024/ Midterm 2, Solutions
- 2024/ Final, Solutions
- 2024/ Topics: Integer properties, Logic of Propositions, Logic of Predicates. Proofs, Sets, Floor and Ceiling Functions,
Injection, Surjection, Bijection, Inverse Functions, Asymptotic Analysis (Big-Oh), Algorithm Analysis, Finite-state machines,
Sequences, Summation. Induction, Recursive definitions, Structural Induction, Iterative and Recursive algorithms, Program Correctness,
Master Theorem, Recurrence Relations, Relations on sets, Equivalence relations, Partial orders, Enumeration, Pengionhole Priciple,
Binomial Coefficients, Graphs, Trees.
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Math/Comp Sci/E C E 435: Introduction to Cryptography
Have taught Spring 2024
- 2024/ Syllabus
- 2024/ Midterm , Solutions
- 2024/ Final , Solutions
- 2024/ Topics: Shift Cipher, Modular Arithmetic, Affine Ciphers, Euclidean Algorithm, Inverse modulo N,
Monoalphabetic and Polyalphabetic Ciphers, Matrices modulo N, Transposition Ciphers, Intro to Cryptanalysis, Probabilistic Model,
Key Enumeration, Chosen Plaintext Attacks, Known plaintext attacks, Ciphertext-only cryptanalysis, Monoalphabetic Cryptanalysis,
Letter Frequencies, Polyalphabetic Cryptanalysis: Kasiski's Test, Coincidence Index, Entropy, Key equivocation, Perfect Secrecy,
Stream Ciphers, The One-time Pad Linear and Non Linear Feedback Shift Register Sequences, Block Ciphers, Operation Modes,
Feistel cipher, DES, Birthday Attacks and Multiple Encryption, Finite Fields, AES, Big Number Arithmetic, Public Key Cryptography,
RSA System, Discrete Logarithms, Diffie-Hellman Key Exchange, Cyclic groups, Elgamal encryption scheme, Elliptic curves,
Digital Signatures via RSA, The Elgamal digital signature scheme, Cryptographic Hash Functions, Authentication in Networks, Kerberos.
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Math 467: Introduction to Number Theory
Have taught Fall 2023
- 2023/ Syllabus
- 2023/ Exam 1, Solutions
- 2023/ Exam 2, Solutions
- 2023/ Exam 3, Solutions
- 2023/ Exam 4, Solutions
- 2023/ Topics: Mathematical Induction, the Binomial Theorem, the Division Algorithm, the Greatest Common Divisor,
the Euclidean Algorithm, the Diophantine Equation $ax + by = c$, the Fundamental Theorem of Arithmetic, the Sieve of Eratosthenes,
the Theory of Congruences, Binary and Decimal Representations of Integers, Linear Congruences, the Chinese Remainder Theorem,
Fermat's Little Theorem, Pseudoprimes, the Sum and Number of Divisors, The Mobius Inversion Formula, the Greatest Integer Function,
Euler's Phi-Function, Euler's Theorem, The Pythagorean Triples, Fermat's Last Theorem for $n=4$, the Fibonacci Sequence,
the Fibonacci Sequence modulo n.
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Math/Comp Sci/Stat 475 Introduction to Combinatorics
Have taught Fall 2023, Fall 2021, Spring 2021, Fall 2020
- 2023/ Syllabus
- 2023/ Midterm 1, Solutions
- 2023/ Midterm 2, Solutions
- 2023/ Final, Solutions
- 2023/ Topics: Basic counting principles, k-permutations and k-combinations of sets,
Permutations and combinationcs of multisets, Probability, Pigeonhole Principle, Inversions, Lexicographic order,
Reflected Gray code, Binary Relations, Partial orders, Equivalence relations, Binomial Coefficients, Sperner Theorem,
Multinomial Theorem, Newton's Binomial Theorem for integer exponents, Inclusion-Exclusion Formula and Applications,
Forbidden positions, Fibonacci sequence, Generating Functions, Exponential Generating Functions, Linear recurrence relations,
Stirling numbers, Partition numbers, Basic Properties of Graphs, Paths and Connectivity, Eulerian Trails,
Hamiltonian paths and cycles, Bipartite graphs, Graph Colorings, Ramsey Theory, Permutations Groups, Burnside's Theorem,
Polya Counting.
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Math/Hist Sci 473 History of Mathematics
Have taught Spring 2023
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Math 222 Calculus and Analytic Geometry II
Have taught Spring 2023, Spring 2022
- 2023/ Syllabus
- Ask our Calculus coordinator about materials
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Math 211 Calculus
Have taught Fall 2022
- 2022/ Syllabus
- Ask our Calculus Coordinator about materials
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Math 461 College Geometry
Have taught Spring 2022, Spring 2021