math-tutor

Included with Lifetime

$97 forever

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.

General

What this skill does


# Mathematics Subject Expert

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

## Topic Coverage

```mermaid
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](references/formulas.md)
- **Calculus:** See [calculus.md](references/calculus.md)
- **Linear Algebra:** See [linear-algebra.md](references/linear-algebra.md)
- **Statistics:** See [statistics.md](references/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

| Strategy | When to Use | Example |
|----------|-------------|---------|
| Direct Proof | Show P → Q directly | "If n is even, n² is even" |
| Contradiction | Assume ¬Q, derive contradiction | Proving √2 is irrational |
| Contrapositive | Prove ¬Q → ¬P instead | Logical equivalence |
| Induction | Statements about all n ∈ ℕ | Sum formulas |
| Cases | Different scenarios | Piecewise functions |

### 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

| Symbol | Meaning |
|--------|---------|
| ∀ | For all |
| ∃ | There exists |
| ∈ | Element of |
| ⊂ | Proper subset |
| ⊆ | Subset or equal |
| ∪ | Union |
| ∩ | Intersection |
| ℕ | Natural numbers {1,2,3,...} |
| ℤ | Integers {...,-1,0,1,...} |
| ℚ | Rational numbers |
| ℝ | Real numbers |
| ℂ | Complex numbers |
| ∞ | Infinity |
| ∴ | Therefore |
| ∵ | Because |
| ∎ | QED (proof complete) |

---

## 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

Files: 5

Size: 14.0 KB

Complexity: 34/100

Category: General

Source: https://github.com/szeyu/vibe-study-skills/tree/main/skills/math-tutor

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