01:47

Visualize Factor Group D4/{R0,R180} Cayley Table from D4 Cayley Table

23:51

U(32)/{1,15} Factor Group Example: What is it Isomorphic to?

17:38

ELON MUSK Pays You $31.69 EVERY SECOND EVERY DAY for 10 years! Calculus for PRESENT & FUTURE VALUES?

11:19

Calculus 2, Lec 18D: Water Pressure & Total Force on the Three Gorges Dam by Integration

08:46

Calculus 2, Lec 18C: Work Done to Pump Water Out of a Cylindrical Tank

07:56

Work Done to Lift an Anchor (using Weighted Chain)

16:56

Double Integral for Mass of Thin Rectangular Plate

04:24

KEYS to PROVING SL(2,ℝ) ⊲ GL(2,ℝ): Determinant Properties! (and Normal Subgroup Test)

07:45

NORMAL SUBGROUPS! Definition of Normal Subgroup and Normal Subgroup Test

10:16

Is U(55) ≈ U(75)? Use Direct Products of Groups to Find Out!

08:30

Work Done by a Variable Force (Work Done to Compress a Spring)

03:52

HOW NERDY! Work Done by Constant Force Against Gravity (Calculator Holding vs Calculator Lifting)

10:23

Find MASS of the ATMOSPHERE with CALCULUS!!! (to Height of 100 Meters)

10:07

Calculus 2, Lec 17B: Radially Symmetric Circle City Population (Integrate 2πr*Population Density)

19:07

Calc 2, Lec 17A: Find Mass and Center of Mass for δ(x) = 1+x g/cm^2 (Density of Isosceles Triangle)

03:18

How to Count Elements of Orders 3 and 9 in ℤ3 ⊕ ℤ9 (Use LCM of Components)

10:38

How Many Elements of Order 2 are in ℤ8, ℤ2 ⊕ ℤ4, and ℤ2 ⊕ ℤ2 ⊕ ℤ2?

15:42

What's the Secret Sauce of the Orbit Stabilizer Theorem Proof?

09:29

Orbit Stabilizer Theorem Example

07:34

Calc 2, Lec 16C: How to Find the Center of Mass (Centroid) of a Lamina with Constant Density

24:20

Calc 2, Lec 16B: Thin Rod & Discrete Masses, Moments, & Center of Mass

27:34

Calculus 2, Lec 16A: Parametric Curve Arc Length Integral Example (with Position & Velocity Vectors)

09:45

Introduction to External Direct Products in Group Theory with Example: ℤ2 ⊕ ℤ3

06:29

Alternating Group A4 has No Subgroup of Order 6 (No Subgroup of Index 2)

05:54

Logical Converse of a Statement

09:41

Corollaries of Lagrange's Theorem in Group Theory

04:23

Group Theory Classification! |G|=p ⇒ G is Cyclic (p is Prime) | Prove with Lagrange's Theorem

10:37

Calc 2, Lec 15F: Area Swept Out by a Polar Curve (includes Infinitesimal Approach w/ dA for sector)

10:51

Calculus 2, Lec 15E: Arc Length of a Polar Curve (Elliptic Function Needed to Evaluate for Limaçon)

07:14

Calculus 2, Lec 15D: Slope of a Polar Curve (Slope ≠ f'(θ)!!!!)

09:30

Polar Graph as Parametric Curve (Angle θ is the Parameter)

13:18

How to Graph a Polar Equation | Graph a Limaçon (Graph r=f(θ)=2+4cos(θ))

10:33

Polar Coordinates Basic Introduction, Conversion Equations and Plotting Points in Polar Coordinates

15:27

Fundamental Properties of Cosets and Their Proofs in Abstract Algebra

16:15

If G and H are Isomorphic Groups, then Aut(G) and Aut(H) are Isomorphic Groups

17:52

Calculus 2, Lec 14E: Review for Exam 1

05:16

Calculus 2, Lec 14D: Arc Length of a Lissajous Figure (use Wolfram Mathematica)

12:30

Calc 2, Lec 14C: Find Arc Length of the Curve y=ln(1+x) from x=0 to x=2 (Use Wolfram Mathematica)

09:00

Calc 2, Lec 14B: ARC LENGTH FORMULA DERIVATION! (Riemann Sum vs Infinitesimal Approaches)

11:25

Calculus 2, Lec 14A: A Simple Solid of Revolution (Riemann Sum vs Infinitesimal Approach to Volume)

07:57

Lagrange's Theorem and All Subgroups of the Dihedral Group D4 of Order 8

06:48

When Do Two Elements of a Group G Induce the Same Inner Automorphism? The CENTER of G is the Key!

20:50

Why is Aut(G) a group? Why is Inn(G) a subgroup of Aut(G)?

10:25

Calculus 2, Lec 13C: Volume of Solid with Triangular Cross-Sections

25:05

Calc 2, Lec 13B: TWO Solid of Revolution Volumes (About Horizontal & Vertical Lines)

20:28

Calculus 2, Lec 13A: Volume of a Pyramid by Slicing and Integration (Riemann Sums & Infinitesimals)

09:50

Preimage of a Subgroup is a Subgroup (Use One Step Subgroup Test)

24:26

Isomorphism is an Equivalence Relation on Groups

08:46

Calculus 2, Lec 12D: Volume of a Cone by Slicing & Integrating (Riemann sum & infinitesimal methods)

19:50

Calculus 2, Lec 12C: Riemann Sum vs Infinitesimal Approach (Integrate to Find Area of 1/4 Circle)

12:12

Calc 2, Lec 12B: NASTY-Looking Improper Integral! Does It Converge or Diverge? Prove Your Answer!

20:33

Calc 2, Lec 12A: How to Make a Probability Distribution with x*e^(-λ*x) for x＞0 (Improper Integral)

12:38

Abstract Algebra Topics to Expect on Exam 1 on Basic Group Theory

04:34

TRIVIAL or TOO TRICKY?? Prove φ(e) = e̅ (φ : G → G̅ is a Group Isomorphism)

17:42

Group Isomorphisms: Definition and Examples

02:33

How Many Elements Have Order 12 in the Symmetric Group S7?

09:44

How Many Permutations Have Order 2 in A8? (Alternating Group on 8 Objects)

03:55

⚡QUICK⚡ and RIGOROUS Proof That Improper Integral Converges (Use Comparison Test)

08:04

PI DAY MAGIC! I Just Happened to Upload This on PI DAY! 🥧 (UNPLANNED!...No Joke, I'm Serious!)

10:11

Calculus 2, Lec 11A: Improper Integral ESSENTIAL FACTS (Includes Type 1 and Type 2 p-Integrals)