Isaacjc08

Package of the notes for undergraduate Linear Algebra, Advanced Linear Algebra, Abstract Algebra 1 and Abstract Algebra 2

Notes taken in a two semester sequence of undergraduate Abstract Algebra (using Gallium text). Including definitions, theorems and proofs, as well as examples. Covered Material: - Division Algorithm - Groups and Abelian Groups - Cyclic Groups - Permutations and Permutation Groups - Subgroups and Normal Subgroups - Cosets and Quotient Groups - Rings and Integral Domains - Abstract Vector Spaces - Ideals and Quotient Rings - Polynomial Rings and Prime Polynomials - Fields and Extensi...

Course notes taken in an undergraduate course in Advanced Linear algebra including advanced topics in elementary linear algebra, in a proof based format, including definitions, theorems and proofs as well as examples. Covered Topics: - Abstract Vector Spaces and Subspaces - Span, Basis, and Linear Independence - Linear Transformations - Matrices and Determinants - Complex Vector Spaces and the Hermitian Dot Product - Inner Products and Inner Product Spaces - Positive Definite Matric...

A re-upload of class notes taken in an undergraduate Linear Algebra prerequisite course. Covering the basics of linear algebra including: - Vectors - Vector Spaces - Matrices (and Augmented Matrices) - Matrix Operations (including Matrix Multiplication) - Row Reduction - Solution Sets (and Set Builder Notation) - Homogeneous Solution Sets - Rank and Rank Space - Null Space - Rank-Nullity Theorem

Legible, well-formatted notes including material covered in a two-semester sequence of Undergraduate Real Analysis. Including theorems, proofs, and examples. Covering (chronologically): - The Axiom of Completeness - Properties of the Real Numbers - Supremums, Infimums, Minimums, and Maximums - Sequences - Series - Functions - Limits (Epsilon-Delta) - Derivatives - Integrals - Inner Products - Measure Theory - Lebesgue Measures - Lebesgue Integrals

Class Notes taken by independent study following traditional Calculus III course

Includes Calculus I notes, Calculus II notes, as well as a comprehensive Identities Sheet. -Calculus I: Limits, Derivatives, and Basic Integration -Calculus II: Advanced Derivatives/Integration, Taylor Series/Polymomials -Identities: Angle Identities, Common Calculus Identities **Calculus III will be included soon

48 Pages of Notes taken in my free time following Professor Leonard’s Calculus 2 course on YouTube. Beginning with Differentiation/Integration of Exponential Functions, followed by advanced techniques of integration such as Integration by Parts, Trig. Substitution, Partial Fraction decomposition. Continues to Improper Integrals, into Sequences and Series. Expands on Taylor/MacLauren Series, as well as various tests of convergence (Integral Test, Ratio Test, etc.). Additionally, opens discussio...

38 Pages of Notes taken in my spare time following Professor Leonard’s calculus 1 course on YouTube. Formally defining the Fundamental Theorem of Calculus. Beginning with an introduction to Limits, followed by definition of a derivative. Continues with Chain Rule, Product Rule, Quotient Rule, Power Rule, etc. Additionally, it includes the definition of an integral as a Riemann Sum, as well as basic integration through an Antiderivative, and u-substitution. Followed by Volume of solids of ...