03:00

Finding the arc length of a function on an interval

03:36

Trigonometric Identity involving arctan and pi

03:05

A Probability Question (drawing balls from a box)

04:49

Finding the line of best fit (least squares regression line) of a set of points

04:15

A trigonometric identity involving the tan function a triangle ABC

07:40

Finding the maximum possible area of a rectangle inscribed in a unit circle

03:57

Proving a binomial sum identity

02:49

Problems involving the product-to-sum formula trigonometry

04:48

Finding the coefficient of x^3 in (2x-1)(3x-2/x)^5 using the binomial expansion

05:59

Finding the radius of convergence of a power series using the ratio test

05:58

Solving a second order linear differential equation using variation of parameters

04:32

Evaluating the definite integral of x^2 / (e^x+1) from -2 to 2

04:59

Finding the arc length of one arch of a cycloid

04:19

Solving a first order linear differential equation with the integrating factor method

04:51

Choosing subsets of a set where no two sets are disjoint

05:30

Choosing n+1 distinct positive integers from a set of 2n positive integers

06:16

Finding whether or not the limit of a two variable function exists

03:02

Finding 1000 consecutive numbers that are composite

02:32

Find the factorisation of x^4+4y^4

03:43

Proof of the Quadratic Formula

04:27

Linear Algebra - Finding the Orthogonal Complement of a subspace

08:27

A proof of Heron's formula for the area of a triangle

05:24

Proof that the angle bisectors of a triangle are concurrent

08:15

A proof that the number e ~ 2.718... is irrational

05:27

Finding the sum of the first n cube numbers using mathematical induction

01:46

Maths Probability problem - Two digit numbers divisible by eight

03:40

Finding the equation of the tangent line to the curve of a rational function at a point

04:32

Classify discontinuities of a function (removable, infinite, jump)

06:01

Calculus - Finding discontinuities of a piecewise function

04:37

Coordinate Geometry - Prove that a circle is tangent to a line

07:05

Does the limit of this piecewise function exist at x = 0?

05:11

Finding a limit of a piecewise function involving rational and irrational numbers

05:04

Find all values of "a" such that this limit exists

04:49

Calculus limit problem with square roots

02:57

Finding the greatest common divisor of two numbers with the euclidean algorithm

04:21

Calculus Limit problem involving a chord and arc of a circle

02:25

Minimum vertical distance between two parabolas

02:44

Maximise and Minimise a cubic polynomial over an interval

07:16

Differentiation Problem involving a piecewise function

10:10

Finding the 100th power of a 2x2 matrix

04:43

Lots of logs and e's from the 2020 MIT Integration Bee Qualifiers

06:56

A graphing problem involving absolute values and a quadratic

05:51

Finding whether a set is a subspace of R^3

10:23

A proof of the AM-GM inequality

12:14

Proof that a spanning set of vectors with the same size as a basis is itself a basis

06:54

Modular Arithmetic - solving a system of linear congruences

04:56

Algebraic equation with four variables a, b, c, d

06:11

Write a vector as a linear combination of three other vectors

08:08

Proof that a finite spanning set of vectors can be reduced to a basis

08:15

Finding the roots of a cubic using the rational root test

07:24

Proving that there are infinitely many primes of the form 4n+3

08:55

A trigonometric identity involving arctan() and Pi

14:13

Proof that you can extend a linearly independent set of vectors to a basis

04:37

Finding the LU factorisation of a matrix

14:22

Proving that a set of matrices form a group with respect to matrix multiplication

11:23

Proof that a linearly independent set of vectors with the same size as a basis is also a basis.

15:41

Finding all Pythagorean Triples

09:56

Proof that any basis for a vector space has the same number of vectors

04:36

Integral of sin(sqrt(x)) from the 2019 MIT Integration Bee Qualifiers

04:56

Proving an Inequality using the Mean Value Theorem