Канал: Mohamed Omar

Trigonometric System of Equations

Trigonometric System of Equations

Recurrence Relation, Two-Term

Recurrence Relation, Two-Term

Math 55 Fall 2022 Oct 20th: Combinatorial Proofs

Math 55 Fall 2022 Oct 20th: Combinatorial Proofs

Math 55 Fall 2022: Oct 6 Class on Fundamentals of Counting

Math 55 Fall 2022: Oct 6 Class on Fundamentals of Counting

Lecture 14b Bipartite Graphs

Lecture 14b Bipartite Graphs

Lecture 14c Coloring Planar Graphs

Lecture 14c Coloring Planar Graphs

Lecture 14a Introduction to Graph Coloring

Lecture 14a Introduction to Graph Coloring

Convex: Local vs Global Minimum

Convex: Local vs Global Minimum

Invariants and Monovariants

Invariants and Monovariants

Vieta's Formula

Vieta's Formula

Nonstandard Math Induction

Nonstandard Math Induction

Putnam Induction | A Nice Induction Problem from the Putnam Exam 2005 A1

Putnam Induction | A Nice Induction Problem from the Putnam Exam 2005 A1

An UNUSUAL Induction Technique | Two Variable Induction

An UNUSUAL Induction Technique | Two Variable Induction

Math Induction Trick RARELY taught in class!

Math Induction Trick RARELY taught in class!

SHOCKING surprise about Binomial Sums and a well-known sequence!

SHOCKING surprise about Binomial Sums and a well-known sequence!

Big O Notation Finally Explained

Big O Notation Finally Explained

International Mathematics Competition 2020 Day 2 Problem 1 | A Derivative Inequality

International Mathematics Competition 2020 Day 2 Problem 1 | A Derivative Inequality

Euler Totient Function

Euler Totient Function

Math with Tahoe!!

Math with Tahoe!!

Contraction Mapping Theorem & Finding Fixed Points of Functions

Contraction Mapping Theorem & Finding Fixed Points of Functions

How I Make Exams

How I Make Exams

Which Polynomials Satisfy This?

Which Polynomials Satisfy This?

What's The Sum of the First N 4th powers?

What's The Sum of the First N 4th powers?

Binomial Theorem Secrets

Binomial Theorem Secrets

Putnam 2003 A3 | Minimize a Sum of Trig Functions

Putnam 2003 A3 | Minimize a Sum of Trig Functions

SURPRISING Limit Techniques!!

SURPRISING Limit Techniques!!

A Problem I've Been Stuck on for 7 Years!!!

A Problem I've Been Stuck on for 7 Years!!!

A Fibonacci Sequence Mystery?!?!?

A Fibonacci Sequence Mystery?!?!?

Can't Do Math Research Without This! The Online Encyclopedia of Integer Sequences

Can't Do Math Research Without This! The Online Encyclopedia of Integer Sequences

Why the Mean Value Theorem matters!

Why the Mean Value Theorem matters!

How To Solve Cubic Equations

How To Solve Cubic Equations

Why Matrices Behave Weirdly | Introducing the Minimal Polynomial

Why Matrices Behave Weirdly | Introducing the Minimal Polynomial

Why Calculus Helps Us Solve Inequalities

Why Calculus Helps Us Solve Inequalities

When Mathematician Meets Finance. A Funny Story of Me With My Friend!

When Mathematician Meets Finance. A Funny Story of Me With My Friend!

Infinitely Many Primes & Why I DON'T Like Euclid's Proof

Infinitely Many Primes & Why I DON'T Like Euclid's Proof

Putnam 2020 A2 | Viewer Suggested: Binomial Sum, But Skewed

Putnam 2020 A2 | Viewer Suggested: Binomial Sum, But Skewed

What is a Convex Set?

What is a Convex Set?

A Problem from My Research!

A Problem from My Research!

How I Make Math Contest Problems

How I Make Math Contest Problems

PI DAY SPECIAL!!! Why is pi is irrational anyway?

PI DAY SPECIAL!!! Why is pi is irrational anyway?

What is Group Theory Anyway???

What is Group Theory Anyway???

Why is e irrational anyway????

Why is e irrational anyway????

Putnam Exam Extravaganza!!! | Solutions to 15 Putnam Exam Problems

Putnam Exam Extravaganza!!! | Solutions to 15 Putnam Exam Problems

Pigeonhole Principle | Putnam Pigeonhole Problems

Pigeonhole Principle | Putnam Pigeonhole Problems

Central Limit Theorem Proof | An Outline of Why The Central Limit Theorem Works

Central Limit Theorem Proof | An Outline of Why The Central Limit Theorem Works

Putnam & International Mathematics Competition Integral Inequalities

Putnam & International Mathematics Competition Integral Inequalities

Sums by Integrals

Sums by Integrals

Is a Positive Polynomial FORCED to be a Sum of Squares??

Is a Positive Polynomial FORCED to be a Sum of Squares??

Putnam Exam A2 | Two Problem A2s from the Putnam

Putnam Exam A2 | Two Problem A2s from the Putnam

Fractional Part Function | Floors & Fractional Parts

Fractional Part Function | Floors & Fractional Parts

Fermat's Last Theorem ...... But for Polynomials!

Fermat's Last Theorem ...... But for Polynomials!

This Is An Integer???? | Cube Roots on Display

This Is An Integer???? | Cube Roots on Display

Cauchy Schwarz Inequality | Applications to Problems, and When Equality Occurs

Cauchy Schwarz Inequality | Applications to Problems, and When Equality Occurs

Putnam Exam 1986 A1 | Maximization Under Constraint

Putnam Exam 1986 A1 | Maximization Under Constraint

CMO 1999 | A quadratic floor function equation

CMO 1999 | A quadratic floor function equation

Cauchy Bound | Bounding Roots of Polynomials

Cauchy Bound | Bounding Roots of Polynomials

Gamma Function and Factorials

Gamma Function and Factorials

Problem on Cyclic Quadrilaterals | Minimizing the Diameter

Problem on Cyclic Quadrilaterals | Minimizing the Diameter

Putnam Exam 2019 B5 | Lagrange Interpolation

Putnam Exam 2019 B5 | Lagrange Interpolation

Putnam Exam 2006 B1

Putnam Exam 2006 B1

Fibonacci Polynomials | Generating Series, Formulas & Identities

Fibonacci Polynomials | Generating Series, Formulas & Identities

A Surprising Trigonometric Expression!

A Surprising Trigonometric Expression!

Eisenstein's Criterion, Irreducible Polynomials & IMO 1993 #1

Eisenstein's Criterion, Irreducible Polynomials & IMO 1993 #1

Trigonometric Integral | Symmetry For The Win!

Trigonometric Integral | Symmetry For The Win!

RSA Cryptography Example | Road to RSA Encryption #10

RSA Cryptography Example | Road to RSA Encryption #10

Rectangle In A Semicircle

Rectangle In A Semicircle

The Tangent Trick for Olympiad Inequalities

The Tangent Trick for Olympiad Inequalities

RSA Cryptography | Road to RSA Encryption #9

RSA Cryptography | Road to RSA Encryption #9

Euler's Theorem | Road to RSA Encryption #8

Euler's Theorem | Road to RSA Encryption #8

Jensen's Inequality: How to Use It

Jensen's Inequality: How to Use It

Chinese Remainder Theorem & Linear Congruences | Road to RSA Encryption #7

Chinese Remainder Theorem & Linear Congruences | Road to RSA Encryption #7

Putnam Exam 2005 A5

Putnam Exam 2005 A5

A Combinatorial Surprise! | Using Linear Algebra Unexpectedly

A Combinatorial Surprise! | Using Linear Algebra Unexpectedly

Mobius Inversion | CHMMC 2013 with @MuPrimeMath and @ProfOmarMath

Mobius Inversion | CHMMC 2013 with @MuPrimeMath and @ProfOmarMath

Putnam 2018 A6 Part 4!!!! @Michael Penn vs @ProfOmarMath

Putnam 2018 A6 Part 4!!!! @Michael Penn vs @ProfOmarMath

Putnam 2018 A6 Part 2!!!! @MichaelPennMath vs @ProfOmarMath

Putnam 2018 A6 Part 2!!!! @MichaelPennMath vs @ProfOmarMath

What's the Determinant??

What's the Determinant??

Virginia Tech Regional Math Competition 2017 #4

Virginia Tech Regional Math Competition 2017 #4

Putnam Exam 2002 B3

Putnam Exam 2002 B3

3D Heron's Formula

3D Heron's Formula

An Interesting Inequality

An Interesting Inequality

Modular Arithmetic | Road to RSA Encryption #6

Modular Arithmetic | Road to RSA Encryption #6

Invisible Points

Invisible Points

Prime Numbers | Road to RSA Encryption #5

Prime Numbers | Road to RSA Encryption #5

A Very Fun Trigonometric Sum

A Very Fun Trigonometric Sum

Putnam Exam 2019 B2

Putnam Exam 2019 B2

Sylow Theorem Part 3 | The Sylow Theorems

Sylow Theorem Part 3 | The Sylow Theorems

Alternating Permutations | Counting Up Down Sequences

Alternating Permutations | Counting Up Down Sequences

AM-GM Inequality | Arithmetic Mean Geometric Mean Inequality

AM-GM Inequality | Arithmetic Mean Geometric Mean Inequality

How Many Digits under Multiplication?

How Many Digits under Multiplication?

Mathematical Induction | Road to RSA Cryptography #4

Mathematical Induction | Road to RSA Cryptography #4

Sylow Theorem Part 2 | The Sylow Theorems

Sylow Theorem Part 2 | The Sylow Theorems

A Surprising Radical Equation

A Surprising Radical Equation

Sylow Theorem Part 1 | The Sylow Theorems

Sylow Theorem Part 1 | The Sylow Theorems

Putnam Exam 2019 A2 | Incenter, Median and Angles

Putnam Exam 2019 A2 | Incenter, Median and Angles

Linear Diophantine Equations | Road to RSA Cryptography #3

Linear Diophantine Equations | Road to RSA Cryptography #3

Cambridge Step 3 | 2017 #1 and the Riemann Zeta Function

Cambridge Step 3 | 2017 #1 and the Riemann Zeta Function

Generating Series | Explicit Formula

Generating Series | Explicit Formula

Putnam Exam 1990 A3 | Lattice Pentagons

Putnam Exam 1990 A3 | Lattice Pentagons

Pick's Theorem | Area, boundary points, and interior points.

Pick's Theorem | Area, boundary points, and interior points.

Trigonometric Inequality | Using Calculus to Develop Trigonometric Inequalities

Trigonometric Inequality | Using Calculus to Develop Trigonometric Inequalities

Putnam Exam 2014 A3

Putnam Exam 2014 A3

Indian Math Olympiad 2014 #2 | A floor problem amenable to experimentation

Indian Math Olympiad 2014 #2 | A floor problem amenable to experimentation

Bezout's Lemma | Road to RSA Cryptography #2

Bezout's Lemma | Road to RSA Cryptography #2

Primes Dividing 7777....7 | A Primer to Decimal Expansions

Primes Dividing 7777....7 | A Primer to Decimal Expansions

Partition Identities | Generating Functions 2

Partition Identities | Generating Functions 2

Virginia Tech Regional Math Competition | 2019 Problem 7

Virginia Tech Regional Math Competition | 2019 Problem 7

Euclidean Algorithm | Road to RSA Cryptography #1

Euclidean Algorithm | Road to RSA Cryptography #1

Normal Distribution | 3 Fun Facts About The Normal Distribution

Normal Distribution | 3 Fun Facts About The Normal Distribution

Putnam Exam 2018 B6

Putnam Exam 2018 B6

Rejected from PhD Programs | 3 Tips for Grad School Prep

Rejected from PhD Programs | 3 Tips for Grad School Prep

Fermat's Little Theorem | A Proof of Fermat's Little Theorem from Number Theory

Fermat's Little Theorem | A Proof of Fermat's Little Theorem from Number Theory

Clever Counting Technique | Counting Peaks via Arrays

Clever Counting Technique | Counting Peaks via Arrays

Virginia Tech Regional Math Contest | 2019 Problem 4

Virginia Tech Regional Math Contest | 2019 Problem 4

Generating Function Intro | Counting With Power Series

Generating Function Intro | Counting With Power Series

Putnam Exam 2019 B3

Putnam Exam 2019 B3

GRE Math Subject Test Analysis | Practice Book 1768 Problem 60

GRE Math Subject Test Analysis | Practice Book 1768 Problem 60

Complex Roots | nth Roots of Complex Numbers

Complex Roots | nth Roots of Complex Numbers

sqrt(a+bi) featuring blackpenredpen | Finding square roots of complex numbers.

sqrt(a+bi) featuring blackpenredpen | Finding square roots of complex numbers.

How to Prove Ptolemy's Theorem for Cyclic Quadrilaterals

How to Prove Ptolemy's Theorem for Cyclic Quadrilaterals

Putnam Exam 2007 B5

Putnam Exam 2007 B5

The Power Method for Eigenvalues | Finding the Dominant Eigenvalue and corresponding Eigenvector

The Power Method for Eigenvalues | Finding the Dominant Eigenvalue and corresponding Eigenvector

Geometry Problem | Illuminating Multiple Solutions and Multiple Perspectives

Geometry Problem | Illuminating Multiple Solutions and Multiple Perspectives

Non-Standard Derivative | What is The Definition of the Derivative Good For?

Non-Standard Derivative | What is The Definition of the Derivative Good For?

Pell's Equation | Approximating Square Root 2 using Pell's Equation

Pell's Equation | Approximating Square Root 2 using Pell's Equation

Fundamental Theorem of Calculus Examples | Math Subject GRE Problems on the Fundamental Theorem

Fundamental Theorem of Calculus Examples | Math Subject GRE Problems on the Fundamental Theorem

Rank-Nullity Intuition | Rank-Nullity Theorem for Vector Space

Rank-Nullity Intuition | Rank-Nullity Theorem for Vector Space

Math Subject GRE: Complex Numbers, GR 1768 #19 and #27

Math Subject GRE: Complex Numbers, GR 1768 #19 and #27

Catalan Numbers Part I: Counting Triangulations (Part II w/ Michael Penn)

Catalan Numbers Part I: Counting Triangulations (Part II w/ Michael Penn)

Math Subject GRE: GR1768 #43) Parametric Curves: Second Derivatives of Parametric Curves

Math Subject GRE: GR1768 #43) Parametric Curves: Second Derivatives of Parametric Curves

Mantel's Theorem: Extremal Graph Theory Primer, and Intro To Turan's Theorem

Mantel's Theorem: Extremal Graph Theory Primer, and Intro To Turan's Theorem

Compact Sets are Closed and Bounded

Compact Sets are Closed and Bounded

Pile Puzzle | Pile Splitting and an Exciting Formula!

Pile Puzzle | Pile Splitting and an Exciting Formula!

GRE Math Subject Test: GR 1768 #46 | Strange Trigonometric Equation

GRE Math Subject Test: GR 1768 #46 | Strange Trigonometric Equation

Leap Year | Not Every 4 Years!! Feb 29 Special!!

Leap Year | Not Every 4 Years!! Feb 29 Special!!

Probability Surprise! | Probability Problem Turns Into Something Completely Different!

Probability Surprise! | Probability Problem Turns Into Something Completely Different!

Putnam Exam 2005 B6

Putnam Exam 2005 B6

Grad School Success | Secrets of Grad School Success

Grad School Success | Secrets of Grad School Success

Young's Inequality | A Geometric Proof of Young's Inequality

Young's Inequality | A Geometric Proof of Young's Inequality

Putnam Exam 2005 B1

Putnam Exam 2005 B1

Surprising Limit: Integrals in Disguise

Surprising Limit: Integrals in Disguise

Differential Equation: Using Linear Algebra!!

Differential Equation: Using Linear Algebra!!

Math Subject GRE: Exponential Integral

Math Subject GRE: Exponential Integral

Binomial Sum: Summing Every Third Binomial

Binomial Sum: Summing Every Third Binomial

Matrix Determinant Lemma: Computing Determinants Nicely!

Matrix Determinant Lemma: Computing Determinants Nicely!

Putnam Exam 2001 B2

Putnam Exam 2001 B2

Putnam Exam | Integrals on the Putnam Exam

Putnam Exam | Integrals on the Putnam Exam

Triangle Inscribed in Rectangle: An alternate approach to Presh's Problem!

Triangle Inscribed in Rectangle: An alternate approach to Presh's Problem!

Math Subject GRE: Multivariable Local Min, Using Single Variable Calculus!

Math Subject GRE: Multivariable Local Min, Using Single Variable Calculus!

Digit Factorial! Fun with Sums

Digit Factorial! Fun with Sums

Gershgorin Circle Theorem: Where The Eigenvalues Are!!

Gershgorin Circle Theorem: Where The Eigenvalues Are!!

Complicated Integral: A Cool Way!!

Complicated Integral: A Cool Way!!

Exponential Equation: Say What?!?

Exponential Equation: Say What?!?

Putnam Exam 2019 B4

Putnam Exam 2019 B4

Math Subject GRE: Weird Equation!! GR1268 #30

Math Subject GRE: Weird Equation!! GR1268 #30

Math Subject GRE: Arc Length! GR1268 #58

Math Subject GRE: Arc Length! GR1268 #58

Avoid Induction!! Proof by Picture

Avoid Induction!! Proof by Picture

Gauss Lucas Theorem: The Roots Are Where?

Gauss Lucas Theorem: The Roots Are Where?

Putnam Exam 2019 A3

Putnam Exam 2019 A3

This factors?!? | Putnam Exam 2019 A1

This factors?!? | Putnam Exam 2019 A1

Putnam Exam 2019 Solutions

Putnam Exam 2019 Solutions

Surprise Theorem!! Number Theory from Counting

Surprise Theorem!! Number Theory from Counting

Welcome to the Channel!

Welcome to the Channel!

Putnam Exam 2016 A1

Putnam Exam 2016 A1

Putnam Exam 2014 A2

Putnam Exam 2014 A2

Putnam Exam 2009 A1

Putnam Exam 2009 A1

Putnam Exam Tips to Improve Your Score

Putnam Exam Tips to Improve Your Score

Alder Award Plenary Speech | Creativity Amidst Adversity

Alder Award Plenary Speech | Creativity Amidst Adversity

Math Subject GRE: Problem 37 on ETS Practice, GR1268 #37

Math Subject GRE: Problem 37 on ETS Practice, GR1268 #37

Math Subject GRE: Topology and Metric Spaces! GR1268 #42

Math Subject GRE: Topology and Metric Spaces! GR1268 #42

Math Subject GRE: Got Questions??

Math Subject GRE: Got Questions??

Math Subject GRE: Eigenvalues Quickly!

Math Subject GRE: Eigenvalues Quickly!

Math Subject GRE: Strange Functions

Math Subject GRE: Strange Functions

Math Subject GRE: Lin Alg Fast!

Math Subject GRE: Lin Alg Fast!

Math Subject GRE: Fund. Theorem of Calculus GR1268 #32

Math Subject GRE: Fund. Theorem of Calculus GR1268 #32

Math Subject GRE: Eliminating Answers GR0568 #27

Math Subject GRE: Eliminating Answers GR0568 #27

Math Subject GRE: Integrals Are Areas! GR9768 #4

Math Subject GRE: Integrals Are Areas! GR9768 #4

Math Subject GRE: Divisibility Tricks GR9768 #61

Math Subject GRE: Divisibility Tricks GR9768 #61

Math Subject GRE: Taylor Series in Disguise

Math Subject GRE: Taylor Series in Disguise

Math Subject GRE: MultiVar Calc GR8767 #55

Math Subject GRE: MultiVar Calc GR8767 #55

Math Subject GRE: Eigenvalues Computation

Math Subject GRE: Eigenvalues Computation

Math Subject GRE: Bases

Math Subject GRE: Bases

Math Subject GRE: Drawings! GR8767 #20

Math Subject GRE: Drawings! GR8767 #20

Math Subject GRE: Central Limit Theorem

Math Subject GRE: Central Limit Theorem

Math Subject GRE: Green's Theorem

Math Subject GRE: Green's Theorem

Math Subject GRE: Comparing Numbers GR1268 #6

Math Subject GRE: Comparing Numbers GR1268 #6

Math Subject GRE: Quick Limits GR1268 #1

Math Subject GRE: Quick Limits GR1268 #1

Math Subject GRE: Integral Trick

Math Subject GRE: Integral Trick

Math Subject GRE: Use An Example GR8767 #44

Math Subject GRE: Use An Example GR8767 #44