17:49

Multi Calc, Lec 5B: Vector Geometry and Vector Algebra in ℝ^3

27:48

Multi Calc, Lec 5A: 3-Dimensional Space ℝ^3 (including Distance Formula, Spheres, and Hyperboloids)

01:05:51

Multi Calc, Lec 4: Polar Coordinates

13:45

Multi Calc, Lec 3B: Surface Area of Solid of Revolution (from Parametric Curve)

24:16

Multi Calc, Lec 3A: Position & Velocity Vectors, Speed, Distance (Arc Length) for Parametric Eqs

36:10

Multivariable Calculus, Lec 2: Using Mathematica for Parametric Equations & Curves in 2D

28:13

Multivariable Calculus, Lecture 1: Parametric Curves in the Plane ℝ^2

30:24

Review Abstract Algebra in 30 Minutes

36:06

A Galois Group Isomorphic to the Symmetric Group S3

23:38

Find the Subfield Lattice of ℚ(√3,√5) over ℚ by Using Galois Theory!

29:33

Review All of Calculus 2 in 30 Minutes

23:41

Solve dy/dx = y^2 in TWO WAYS!! (Separation of Variables and Power Series Solution)

12:46

Damped Harmonic Oscillator with Complex Eigenvalues (Use Euler's Formula, Diff Eq for Calc 2, Pt 8A)

05:39

The Galois Group Gal(ℚ(∜2,i)/ℚ) has 8 Elements!

14:37

ℚ(∛2) is NOT a Galois Extension of ℚ (Fundamental Theorem of Galois Theory Does NOT Apply)

36:54

Galois Theory: Fundamental Definitions and a Basic Example

08:11

A Sneak Peek at Fourier Series by Playing Sound Waves in Wolfram Mathematica

25:45

How to Model Simple Harmonic Motion for Mass on a Spring (Diff Eqs for Calculus 2, Part 7B)

27:30

WOW! 4 Equilibrium Points! Logistic Growth Competing Species Model (Diff Eqs for Calc 2, Part 7A)

23:59

Galois Field GF(2^3) = GF(8)

27:20

Two Simple Finite Field Examples: ℤ2 and Galois Field GF(2^2) = GF(4)

16:59

Differential Equations for Calculus 2, Pt 6: Intro to Competing Species Model (use Mathematica)

12:28

Find a Splitting Field of x^3-1 over ℚ

20:26

ℚ(√2 + √3) = ℚ(√2,√3)...But WHY??? 🤔

17:32

ℚ(∛5) is an Algebraic Field Extension of ℚ of Degree 3 (so it's a finite degree extension too!)

18:47

Differential Equations for Calculus 2, Part 5B: Predator-Prey Model (Robins and Worms)

42:27

Differential Equations for Calculus 2, Part 5A: Logistic Model for Population Growth

22:56

Can a Polynomial Have Two Splitting Fields over ℚ???

34:01

Field Extensions and Kronecker's Theorem (Fundamental Theorem of Field Theory), including Examples

14:09

Differential Equations for Calculus 2, Part 4B: Free Fall with Air Resistance

18:15

Differential Equations for Calculus 2, Part 4A: Mixing Problem (Compartmental Analysis)

25:38

How to Avoid Going BROKE in Retirement with CALCULUS!

06:10

A Simple Field Extension! ℚ(√2) is a splitting field for f(x)=x^2-2 over the rational numbers ℚ

25:58

Vector Spaces in Linear Algebra vs Abstract Algebra

23:20

Differential Equations for Calculus 2, Part 3: Newton's Law of Cooling

32:25

The Calculus of Drug Dosing

52:52

Abstract Algebra Review for Exam 3

19:21

Finite Field Constructions and Calculations are FUN 🎉 in Abstract Algebra!

01:02:01

Differential Equations for Calculus 2, Part 2: Separation of Variables, Slope Fields, Euler's Method

09:42

Why is x^4+x+1 irreducible over the rationals ℚ? Use the Mod p Irreducibility Test

03:38

Eisenstein's Criterion is Weird!

15:03

Are Irreducible Polynomials Like Prime Numbers?!?

08:47

Polynomial Division Algorithm over a Field and Corollaries (Remainder Theorem, Factor Theorem)

01:05:16

Differential Equations for Calculus 2, Part 1: Basic Models and Separation of Variables

10:09

ℤ[x], ℚ[x], & ℝ[x] Contain ℤ as a Subring while ℤ(x), ℚ(x), & ℝ(x) Contain ℚ as a Minimal Subfield

15:47

Idempotent Elements in a Ring Help Us to Study Ring Homomorphisms

08:10

Natural Projection Homomorphisms Have Kernels That Are Easy to Find!

09:03

Use Evaluation Homomorphism ℤ[x] → ℤ by f(x) ↦ f(0) to Show ＜x＞ is Prime but Not Maximal in ℤ[x]

05:44

Win $1,000,000 by Solving the Hardest Math Problem in the World!

35:51

How to Visualize z^2, 1/z, & e^z as Complex Mappings of the Complex Plane (use Wolfram Mathematica)

19:48

Discover the Geometry of Complex Number Multiplication by Example

07:29

Ring Homomorphism Definition | Preimage φ^-1(K) of a Ring Ideal K (Use Ideal Test)

12:55

Maximal Ideal Definition, Examples, and Relationship to Fields in Abstract Algebra

08:47

Factor Ring R/A is an Integral Domain If and Only If A is a Prime Ideal in R, a Commutative Ring wit

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