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NumeriveMATHUniversity mathematics

UNIVERSITY STUDY LIBRARY

Understand the idea. Justify each step.

Choose a course, then a topic. Each detailed lesson separates definitions, assumptions, derivations, examples and counterexamples, with a short understanding check.

14 course groups · 35 topic guides · English / Chinese. These focused guides support university study; they are not complete semester syllabi.

01

College Algebra & Precalculus Bridge

  1. 01Functions, Domains & Transformations
Course guide & prerequisites →
02

Calculus I: Change & Accumulation

  1. 01Limits & Continuity
  2. 02Derivatives, Chain Rule & Implicit Change
  3. 03Derivative Tests & Optimization
  4. 04Integrals & the Fundamental Theorem
Course guide & prerequisites →
03

Calculus II: Integrals & Series

  1. 01Integration Techniques & Improper Integrals
  2. 02Sequences, Convergence & Taylor Series
  3. 03Parametric & Polar Calculus
Course guide & prerequisites →
04

Multivariable Calculus

  1. 01Partial Derivatives & Directional Change
  2. 02Hessians & Multivariable Extrema
  3. 03Multiple, Line & Surface Integrals
Course guide & prerequisites →
05

Linear Algebra

  1. 01Matrices, Elimination & Inverses
  2. 02Span, Basis, Rank & Nullity
  3. 03Eigenvalues & Orthogonal Projection
Course guide & prerequisites →
06

Ordinary Differential Equations

  1. 01First-Order Equations & Initial Values
  2. 02Second-Order Equations & Linear Systems
  3. 03Laplace Transforms & Euler Steps
Course guide & prerequisites →
07

University Probability & Statistics

  1. 01Random Variables, PMFs, PDFs & CDFs
  2. 02Expectation, Variance & the CLT
  3. 03Estimation, Tests & Regression
Course guide & prerequisites →
08

Numerical Methods

  1. 01Bisection, Newton & Error
  2. 02Interpolation & Numerical Integration
Course guide & prerequisites →
09

Discrete Mathematics

  1. 01Logic, Sets & Relations
  2. 02Graphs, Trees & Discrete Models
Course guide & prerequisites →
10

Introduction to Mathematical Proof

  1. 01Direct, Contrapositive & Contradiction Proofs
  2. 02Induction, Bijections & Countability
Course guide & prerequisites →
11

Real Analysis: First Rigorous Steps

  1. 01Suprema, Epsilon Bounds & Compactness
  2. 02Uniform Continuity & Function Sequences
Course guide & prerequisites →
12

Abstract Algebra: Structures

  1. 01Groups, Subgroups & Cosets
  2. 02Homomorphisms, Kernels & Images
  3. 03Rings, Ideals & Fields
Course guide & prerequisites →
13

Complex Analysis: Analytic Functions

  1. 01Analyticity & Cauchy–Riemann
  2. 02Contour Integrals, Laurent Terms & Residues
Course guide & prerequisites →
14

Linear Optimization

  1. 01Feasible Regions, Vertices & Dual Bounds
  2. 02Integer Decisions, Assignment & Transport
Course guide & prerequisites →
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