MathDoctorBob

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My latest project has been a series of short articles on Algebraic Combinatorics for beginners (K-12 and up). No Calculus needed. Pdfs available at the link. Girls' Angle Bulletin: www.girlsangle.org February/March 2022: Shortcuts to Counting April/May 2022: Pascal's Identity, the Binomial Theorem, and Chu-Vandermonde Convolution June/July 2022: Central Binomial Coefficients and Catalan Numbers August/September 2022: Fibonacci Numbers and Multi

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Rogue Schoolers

Member · since 2026

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Research talk (11/12/2021): Lattice path enumeration for semi-magic squares of…

YouTubeNov 13, 2021

INTALG 2.2: Graphs of Functions

YouTubeAug 22, 2020

INTALG 3.1. Systems of Linear Equations (2 Variables)

YouTubeAug 21, 2020

INTALG 2.5: Point-Slope Equation of a Line

YouTubeAug 21, 2020

INTALG 2.4: Lines and Slope

YouTubeAug 21, 2020

INTALG 2.1: Functions

YouTubeAug 21, 2020

CANT 2020: Semi-magic matrices for dihedral groups

YouTubeJun 4, 2020

INTALG 6.1: Rational Expressions: Basics

YouTubeApr 24, 2020

INTALG 6.2: Rational Expressions: Addition

YouTubeApr 24, 2020

INTALG 6.6: Solving Rational Equations

YouTubeApr 23, 2020

INTALG 6.3: Nested Rational Expressions

YouTubeApr 19, 2020

INTALG 9.5: Solving Exponential and Logarithmic Equations

YouTubeApr 13, 2020

INTALG 9.1: Exponential Functions

YouTubeApr 13, 2020

INTALG 9.4: Rules for Logarithms

YouTubeApr 9, 2020

INTALG 9.3: Logarithms

YouTubeApr 9, 2020

INTALG 5.4: Factoring Quadratic Polynomials

YouTubeApr 5, 2020

INTALG 8 3: Quadratic Functions and Parabolas

YouTubeApr 5, 2020

INTALG 5.3: Factoring by Grouping

YouTubeApr 4, 2020

INTALG 5.7: Solving Equations by Factoring

YouTubeApr 4, 2020

INTALG 5.5: Special Forms of Factoring

YouTubeApr 2, 2020

INTALG 4.1: Linear Inequalities

YouTubeApr 1, 2020

INTALG 4.2: Compound Inequalities

YouTubeApr 1, 2020

INTALG 8.2: The Quadratic Formula

YouTubeMar 29, 2020

INTALG 8.1b: Completing The Square

YouTubeMar 29, 2020

INTALG 8.1a: Square Root Property and Applications

YouTubeMar 29, 2020

INTALG 4 3: Absolute Value Equalities

YouTubeMar 29, 2020

INTALG 1.6b: Exponent Rules (Part 2)

YouTubeMar 28, 2020

INTALG 1.6a: Exponent Rules (Part 1)

YouTubeMar 28, 2020

INTALG 7.7: Complex Numbers

YouTubeMar 25, 2020

INTALG 7 6: Radical Equations

YouTubeMar 25, 2020

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Techniques

Beyond the Basics: Taming Integrals with Partial Fractions

Partial fractions can seem intimidating, but understanding how they break down complex rational functions is a key step toward mastering the art of integration.

MathDoctorBob

Rogue Math

4 min

0 0 09 days ago

Techniques

When Math Gets Tricky: Handling Absolute Values in Calculus

Dealing with absolute values in integration requires more than just formula application; it demands a geometric understanding of how to partition the region and apply the Fundamental Theorem of Calculus.

MathDoctorBob

Rogue Math

4 min

0 0 010 days ago

Techniques

When Algebra Meets Calculus: Conquering Partial Fractions with Quadratic Factors

Partial fractions can feel like a labyrinth, but by mastering the techniques of substitution and algebraic verification, even the most complex integrals yield to a systematic approach.

MathDoctorBob

Rogue Math

4 min

0 0 011 days ago

Techniques

When Matrices Click: Mastering Cramer's Rule in Z/p

Linear algebra can feel like a massive leap, but understanding Cramer's Rule over finite fields is a monumental step. We'll break down the process of solving systems of equations using determinants.

MathDoctorBob

Rogue Math

4 min

0 0 012 days ago

Science

Unmasking Symmetry: The Elegant Dance Between Groups and Fields

Dive into the heart of Galois Theory, exploring how automorphisms connect the abstract world of group theory to the concrete structures of field extensions.

MathDoctorBob

Rogue Math

3 min

0 0 013 days ago

Techniques

Beyond the Basics: Mastering Definite Integrals and Logarithmic Transformations

Calculus can feel abstract, but with the right approach—and a personalized tutor—even complex definite integrals involving logarithms and exponential bases will finally click.

MathDoctorBob

Rogue Math

4 min

0 0 014 days ago

Science

Beyond the Graph: When Math Moves from Geometry to Proof

Dive into the world of infinite series and the Integral Test. Understanding convergence is a major step toward becoming a First Proof.

MathDoctorBob

Rogue Math

4 min

0 0 015 days ago

Science

Sketching Structure: How Mathematical Traces Teach Composition and Form

Before you pick up a brush, you must learn to see the skeleton of the subject. We dive into how complex visualization exercises teach foundational skills in composition and perspective.

MathDoctorBob

Rogue Artists

4 min

0 0 016 days ago

Science

From Orbits to Invariants: Unpacking the Logic of Group Theory

We dive into advanced abstract algebra, exploring how concepts like conjugacy classes and characteristic polynomials help us understand the deep structure of finite groups.

MathDoctorBob

Rogue Math

4 min

0 0 017 days ago

Science

Beyond the Straight Line: Unraveling the Formula for Arc Length

Sometimes the most beautiful mathematics deals with curves, not straight lines. We're tackling the derivation of the arc length formula, making calculus feel intuitive and accessible.

MathDoctorBob

Rogue Math

4 min

0 0 018 days ago

Science

Unraveling the Secrets of Simple Groups: Order 168

We're diving deep into Sylow Theory to prove that the simple group of order 168 must be non-abelian. Get ready for a serious challenge!

MathDoctorBob

Rogue Math

4 min

0 0 019 days ago

Techniques

From Domain to Derivative: Mastering the Graph of Fractional Exponents

Calculus can feel overwhelming, but by breaking down the graph of complex functions like f(x) = x^(4/3) - 8x^(2/3), we can build confidence, one critical point at a time.

MathDoctorBob

Rogue Math

4 min

0 0 020 days ago

Science

From Average Speed to Instantaneous: Unpacking the Mean Value Theorem

The Mean Value Theorem is a foundational pillar of calculus, connecting the average rate of change over an interval to the instantaneous rate of change at a specific point.

MathDoctorBob

Rogue Math

4 min

0 0 021 days ago

Techniques

When Visualization Meets Optimization: Finding Spheres with Lagrange Multipliers

Calculus can feel abstract, but by combining geometry with the power of Lagrange multipliers, we can find the equation of complex shapes, proving that visualization and theory always work together.

MathDoctorBob

Rogue Math

4 min

0 0 022 days ago

Techniques

The Art of Working Backwards: Proving a Complex Trig Identity

Proof isn't about knowing the answer; it's about mastering the detective work of mathematics. We break down a challenging precalculus identity step-by-step.

MathDoctorBob

Rogue Math

3 min

0 0 023 days ago

Science

Beyond the Estimate: Mastering Error Bounds with Taylor's Theorem

Calculus can feel like magic, but Taylor's Theorem gives us the rigorous proof and the tools to control estimation error, even when we can't calculate the exact value.

MathDoctorBob

Rogue Math

4 min

0 0 024 days ago

Science

Beyond the Ratio Test: Mastering Convergence with the Root Test

The Root Test is a powerful tool for determining the convergence of tricky series. Let's break down how this calculus concept helps us understand the limits of infinite sums.

MathDoctorBob

Rogue Math

4 min

0 0 025 days ago

Techniques

Finding the Missing Function: Mastering the Antiderivative of Polynomials

Ready to move past basic derivatives? We break down the foundational rules of integration—the Sum and Constant Multiple Rules—to help you find the antiderivative of any polynomial.

MathDoctorBob

Rogue Math

4 min

0 0 026 days ago

Science

How Long Does Radium Last? Decoding Half-Lives with Exponential Decay

Radioactive decay governs everything from planetary formation to your morning coffee. We break down the math behind half-lives, showing how to calculate the decay rate of elements like radium.

MathDoctorBob

Rogue Scientists

3 min

0 0 027 days ago

Science

When Continuity Makes the Impossible Click: Solving Advanced Inequalities

Dive deep into how calculus uses the principle of continuity to solve complex absolute value inequalities, turning intimidating algebra into a visual, graph-based puzzle.

MathDoctorBob

Rogue Math

3 min

0 0 028 days ago

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