07:14

Are Prime Ideals in Ring Theory Related to Prime Numbers???

11:39

Introduction to Complex Numbers!!...in a Calculus Course?!?

11:05

This Function Breaks Taylor Series!

07:55

MATH FUN! 🥳 Taylor Series Animated Graphs in Wolfram Mathematica (They Might Change Your Life)

06:36

BUT WHY Does the Taylor Series for e^x Actually Converge to e^x?? Proof with Lagrange Error Bound

21:42

Calculus 2, Lec 28A: Error in Taylor Polynomial Approximation to e^x

10:43

ℤ3[x]/＜x^2+1＞ is a Field with 3^2=9 Elements (Constructed as a Factor Ring)

08:31

Basic Factor Ring Example: ℤ/4ℤ

05:15

Ring Theory IDEAL SURPRISES!! If 1 ∈ A, then A = R?!? If unit ∈ A, then A = R?!?

05:52

Learn How to Use IDEAL TEST! Prove ＜a1,a2,...,an＞ is an Ideal of a R (a Commutative Ring with Unity)

01:06:13

Calculus 2: What Do I Need to Know for Exam 2? (These Topics are also on the AP Calculus BC Exam)

05:26

Prove Ideal of Polynomials in ℝ[x] with Zero Constant Term is ＜x＞ (Principal Ideal Gen by x)

09:30

Use IDEAL TEST! Prove ＜a＞ = { ra | r ∈ R} is Ideal of Commutative Ring R with 1 (Principal Ideal)

04:16

RING IDEALS! Definition of a (Two-Sided) Ideal and Ideal Test (both have "Super-Closure")

06:15

SURPRISE! An Infinite Ring Can Have Characteristic n (Ex: the Ring of Polynomials ℤn[x] has char n)

11:52

Calculus 2, Lec 26D: Substituting, Multiplying, and Dividing with Taylor Series

08:51

ALIENS 👽👽 AGREE!! This is the MOST BEAUTIFUL EQUATION in the UNIVERSE!!...WHY?!? How to Prove It?

23:37

Calculus 2, Lec 26B: The Most MAGICAL 🧙‍♂️ & FUN 🎉 Taylor Series Examples

22:14

Calculus 2, Lec 26A: Newton's Binomial Series Formula Derived Using Taylor Series Formula

12:15

Field with 9 Elements: Gaussian Integers Mod 3 (ℤ3[i]={a+bi | a,b ∈ ℤ3, i^2 = -1} w/ mod 3 + and *)

26:51

Polynomial Rings with Coefficients from ℤ and ℤn -- WEIRD Things Can Happen When n is Not Prime!

09:08

SUBRING TEST! Prove Strictly Upper Triangular Matrices Form a Subring of M2(ℤ)

55:56

Your First Full TAYLOR SERIES Lecture in Calculus 2

14:20

ℤn is a Strange Ring when n is Not Prime

05:29

Why Does a(-b) = -ab in Ring Theory from Abstract Algebra??

05:01

Power Series has a "CLOPEN" Interval of Convergence?!? Is that a WORD?!? Key Example in Calculus

21:07

Introduction to POWER SERIES with Geometric Series (Interval of Convergence & Radius of Convergence)

17:24

Calculus 2, Lec 24C: Alternating Harmonic Series, Alternating Series Test and Error Bound

07:20

MATH FUN! 🎉 Complicated Ratio Test Problem with Factorials

09:00

∑2^n/(n^3+1): What Happens If We Use BOTH Divergence Test AND Ratio Test?

18:16

Introduction to Ring Theory with Examples in Abstract Algebra (including Subrings)

05:54

Integer Partition Function and Classification of Finite Abelian Groups

07:32

Classify All Abelian Groups of Order 1000, Up to Isomorphism

11:21

Calculus 2, Lec 23F: The MOST IMPORTANT Ratio Test Example in Calculus??

04:51

Calculus 2, Lec 23E: Comparison Test to Prove ∑1/(n^(1/2)-1) Diverges

05:33

Calculus 2, Lec 23D: Comparison Test to Prove ∑1/(n^3+1) Converges

02:09

Use DIVERGENCE TEST FIRST! (and ONLY for Proving DIVERGENCE...NEVER Convergence)

12:27

Calc 2, Lec 23B: Prove Series ∑1/(n*ln(n)) Diverges with Integral Test

12:14

Present Value of Discrete Annuity Due Using Continuous Interest Rate

06:05

How Many Abelian Groups of Order 81=3^4 Are There?

06:02

Prove the First Isomorphism Theorem for Groups

03:46

Preimage of an Element Under a Group Homomorphism is a Coset of the Kernel of the Homomorphism

09:52

How to Count Group Homomorphisms Between Cyclic Groups

02:23

This Should Be Common Cultural Math Knowledge: The Harmonic Series Diverges!

09:16

Why Does the Basel Problem Series ∑1/n^2 Converge to a Number Less Than 2? Integral Test for Series

05:26

Basel Problem, Euler, Zeta Function, Riemann Hypothesis, Cryptography, & Internet are All Connected

13:56

Calculus 2, Lec 22B: CLASSIC TELESCOPING SERIES... ∑1/(n^2+n) = ∑1/(n(n+1)) = 1

31:05

How Much Should I Pay for a LIFE ANNUITY? Use Calculus and Probability to Find the Fair Price

30:19

Calculus 2, Lec 21B: Finite and Infinite Geometric Series

31:13

Theory & Simulation for Actuarial Present Value (Triangular Distribution Lifetime)...Use Mathematica

47:17

Chapter Review from Gallian's Abstract Algebra to Prepare for Exam 2

10:07

Group Theory Problem-Solving: If |G| = p^2, how do we prove |Z(G)| ≠ p (p is prime)?

05:18

Sketch Idea of Proof: Every Group of Order 125 has Element (& Subgroup) of Order 5

23:15

Calculus 2, Lecture 20B: SEQUENCES!

34:42

CDF METHOD is SO POWERFUL! (Find Distribution of Transformed Random Variable for Present Value)

14:16

Group Homomorphisms, Linear Transformations, Kernels, & First Isomorphism Theorem

16:25

What is the Factor Group (ℤ4 ⊕ ℤ12)/＜(2,2)＞ Isomorphic To? (Group Theory)

16:06

ACTUARIES use CALC! Actuarial Present Value of Future Benefit (CDF, PDF, & Mean of Distribution)

46:25

CALCULUS & REFRIGERATORS...WHO KNEW?!? Probability Model (Exponential Distribution Lifetime)

08:01

The G/Z THEOREM is WEIRD! But Its PROOF is INTERESTING!