3-Hour Abstract Algebra LIVE | Homomorphisms, Kernels, Normal Subgroups & Quotient Groups

🔥 3-HOUR ABSTRACT ALGEBRA LIVE — GROUP THEORY WITH WOODY CALCULUS In this long-form live lesson, we build a major sequence of beginning Abstract Algebra and Group Theory concepts step by step. This is the kind of detailed university-level instruction available inside the Woody Calculus Skool community. 📘 TOPICS COVERED: 00 — Group Homomorphisms • Definition of a group homomorphism • φ(ab) = φ(a)φ(b) • Logarithm as a homomorphism from positive real multiplication to real addition Kernel of a Homomorphism • Definition of Ker(φ) • Proving the identity belongs to the kernel • Closure under multiplication • Closure under inverses • Proving Ker(φ) ≤ G Normal Subgroups • Definition of N ◁ G • Left cosets and right cosets • gN = Ng • Conjugation • gng⁻¹ ∈ N • Proving Ker(φ) ◁ G Injectivity • Trivial subgroup • Proving φ is injective ⇔ Ker(φ) = {e_G} Factor Groups / Quotient Groups • Cosets • G/N • Coset multiplication • (aN)(bN) = (ab)N • Why the operation must be well-defined • Closure • Associativity • Identity • Inverses • Complete proof that G/N is a group when N ◁ G 🧠 WOODY CALCULUS METHOD Rewrite each problem while saying what you are writing out loud. Articulate each step with confidence, out loud. Don’t memorize the finished proof. Learn the structure well enough that you can reproduce it from a blank page. Pattern first → setup second → computation third. 🔥 THIS IS WHAT YOU GET WITH WOODY CALCULUS ON SKOOL: Long-form live instruction Detailed proofs Real-time mathematical discussion Handwritten notes Exam preparation Advanced university mathematics Courses and support include: Calculus 2 Calculus 3 Differential Equations Linear Algebra Abstract Algebra Real Analysis and more. 👉 Join Woody Calculus: https://www.skool.com/woodycalculus/a... SEARCH TERMS: Abstract Algebra, Group Theory, group homomorphism, kernel of homomorphism, kernel subgroup, normal subgroup, kernel normal subgroup proof, injective homomorphism, trivial kernel, cosets, quotient groups, factor groups, G/N, well-defined coset multiplication, group theory proofs, Abstract Algebra tutor, university mathematics, Woody Calculus. #AbstractAlgebra #GroupTheory #GroupHomomorphism #Kernel #NormalSubgroup #QuotientGroup #FactorGroup #UniversityMath #WoodyCalculus