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Want the BASICS of Definite Integrals? START HERE!
Differential Equation Mixing Problem: Solution by Integrating Factor, Slope Field, Euler's Method
Derivation of Newton's Forward Difference Formula for Function Interpolation & Excel Implementation
Find Distance for Constant Speed, Constant Acceleration, and Constant Jerk
Lagrange Interpolation Examples, Error Terms, and Warnings (about Extrapolation and Overfitting)
Win $1,000,000 by Solving the Hardest Math Problem in the World!
A Brief Introduction to Galois Theory: Galois Group of ℚ(√2) Over ℚ, Gal(ℚ(√2)/ℚ)
The Hardest Math Class in the World?!?!
Abstract Algebra: Isomorphic Groups have Isomorphic Automorphism Groups
Group of Units U(n) Isomorphism Classes as External Direct Products
External Direct Product of Groups Example: Is ℤ2 ⊕ ℤ2 a Cyclic Group?
Complex Addition and the Parallelogram Law. Use ListPlot on Mathematica to make the plot.
Sketch Van der Pol System Phase Portrait | Existence, Uniqueness, & Flow (Group Property of Flow)
Calc 1, Lec 11A: Prove Power Rule for n = -1/2 and Positive Integers n
First 2 Trigonometric Substitution Examples: Integral of Sqrt(1-x^2) and Integral of Sqrt(1+x^2)
Lagrange Polynomial Interpolation Error Bound Example
Series Convergence and Divergence: Basic Examples, Harmonic Series, p-Series, Integral Test
How Many Abelian Groups of Order 81=3^4 Are There?
A Simple Field Extension! ℚ(√2) is a splitting field for f(x)=x^2-2 over the rational numbers ℚ
Calculus 2, Lec 12C: Riemann Sum vs Infinitesimal Approach (Integrate to Find Area of 1/4 Circle)
How Much Should I Pay for a LIFE ANNUITY? Use Calculus and Probability to Find the Fair Price
Calculus 2, Lec 3A: How to Think About Integrals Conceptually (Flow Rate Example, Linearity)
When Do Two Elements of a Group G Induce the Same Inner Automorphism? The CENTER of G is the Key!
How To Find an Orthonormal Basis for a Subspace of an Inner Product Space
Solving Equations in the Dihedral Group D4 of Symmetries of a Square (Get Perfect Squares & Cubes)
Corollaries of Lagrange's Theorem in Group Theory
If G and H are Isomorphic Groups, then Aut(G) and Aut(H) are Isomorphic Groups
Calculus 2, Lec 22B: CLASSIC TELESCOPING SERIES... ∑1/(n^2+n) = ∑1/(n(n+1)) = 1
Find a Splitting Field of x^3-1 over ℚ
Group Theory Classification! |G|=p ⇒ G is Cyclic (p is Prime) | Prove with Lagrange's Theorem
Basic Modular Arithmetic Example Calculations
Multivariable Calculus, 20 Minute Review of Topics on Exam 1
Abst Alg 11: Orders of Permutations, Isomorphism S3 to D3, Elements & Subgrps of Symmetric Group S4
SURPRISE! An Infinite Ring Can Have Characteristic n (Ex: the Ring of Polynomials ℤn[x] has char n)
Differential Equations for Calculus 2, Part 5B: Predator-Prey Model (Robins and Worms)
Calc 2, Lec 12B: NASTY-Looking Improper Integral! Does It Converge or Diverge? Prove Your Answer!
Introduction to Complex Numbers!!...in a Calculus Course?!?
This Function Breaks Taylor Series!
Differential Equations for Calculus 2, Pt 6: Intro to Competing Species Model (use Mathematica)
Fundamental Theorem of Cyclic Groups is the HAMMER YOU NEED to Do Cyclic Group Proofs!
Calculus 2, Lec 23D: Comparison Test to Prove ∑1/(n^3+1) Converges
Positive Integer Exponents (Powers) as Repeated Multiplication
Prove Square Roots of Non-Perfect Squares are Irrational
Abstract Algebra, Lec 4A: Group Definition, Basic Properties of Groups, Cayley Tables, Observations
Abstract Algebra, Lec 9B: Powers of Cyclic Group Generators, Subgroup Lattice, Permutations
Complex Conjugates, Complex Division, and Visualization on Mathematica.
Distribution of the Sum of Non Independent Random Variables based on Joint Density (PDF)
Mixed Random Variable: Payment Random Variable w/ Deductible (Loss Random Variable is Uniform)
Prove the First Isomorphism Theorem for Groups
Abstract Alg, Lec 17A: Abstract Nonsense :-), Apps of Group Theory, "Products" & Ext Direct Products
