name: math-tutor
description: Mathematics subject expertise for study notes, problem-solving, and explanations. Covers algebra, calculus, statistics, linear algebra, and discrete math. Provides formulas, proof strategies, and step-by-step solutions. Use when studying math topics, creating math notes, solving math problems, or explaining mathematical concepts. Triggers - math help, algebra, calculus, derivatives, integrals, statistics, linear algebra, proofs, equations.

Mathematics Subject Expert

Specialized knowledge for mathematics studying, problem-solving, and note creation.

Topic Coverage

mindmap
  root((Mathematics))
    Algebra
      Equations
      Polynomials
      Functions
      Inequalities
    Calculus
      Limits
      Derivatives
      Integrals
      Series
    Statistics
      Descriptive
      Probability
      Inference
      Distributions
    Linear Algebra
      Matrices
      Vectors
      Eigenvalues
      Transformations
    Discrete Math
      Logic
      Sets
      Combinatorics
      Graph Theory

Quick Reference Links

• Formulas: See formulas.md
• Calculus: See calculus.md
• Linear Algebra: See linear-algebra.md
• Statistics: See statistics.md

Problem-Solving Framework

General Steps

1. Read carefully - Identify what's given and what's asked
2. Draw/visualize - Sketch graphs, diagrams
3. Choose strategy - Direct, substitution, contradiction, etc.
4. Execute - Show all steps clearly
5. Verify - Check answer makes sense

Common Proof Strategies

Mathematical Induction Template

Claim: P(n) is true for all n ≥ 1

Base Case: Show P(1) is true.
[Verify for n = 1]

Inductive Step:
Assume P(k) is true for some k ≥ 1. (Inductive Hypothesis)
Show P(k+1) is true.
[Derive P(k+1) using P(k)]

Therefore, by induction, P(n) is true for all n ≥ 1. ∎

Notation Reference

Function Analysis Checklist

1. Domain - What x values work?
2. Range - What y values result?
3. Intercepts - Where x=0, y=0?
4. Symmetry - Even f(-x)=f(x)? Odd f(-x)=-f(x)?
5. Asymptotes - Vertical, horizontal, oblique?
6. Critical points - Where f'(x)=0 or undefined?
7. Intervals - Increasing/decreasing?
8. Concavity - Where f''(x) > 0 or < 0?
9. Inflection points - Where concavity changes?

Common Mistakes to Avoid

1. Dividing by zero - Check denominator ≠ 0
2. Square root of negative - Consider domain
3. Forgetting ± when taking square roots
4. Chain rule errors in derivatives
5. Forgetting +C in indefinite integrals
6. Incorrect limit laws for 0/0, ∞/∞ forms