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Hi, I'm Dave. I help you learn mathematics and
encourage
you to have fun while you're at it.
LET'S DO SOME MATH
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Newsletter
Finite Affine Planes - Fun Facts and Interesting Information
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
In an Affine Plane, All Lines Have the Same Number of Points
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
The Affine Plane - What It Is and How It Works
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Models of Incidence Planes - Straight Fan Planes
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Models of Incidence Planes - Hand Shake Planes
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Models of Finite Incidence Planes - Young's Geometry
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Models of Finite Incidence Planes - Fano's Geometry
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Models of Incidence Geometry - What Do They Look Like?
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Models of Finite Incident Planes - Hands on
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Why Parallelism in Planes Is So Important
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Incidence Axioms and Basic Theorems
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Every Point Is Incident With at Least Two Distinct Lines
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Every Point Has at Least One Line Not Incident With It
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Every Line Has at Least One Point Not Incident With It
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
There Exist Three Distinct Lines That Are Nonconcurrent
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Every Point Is Incident With at Least One Line
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
Inverse Cosine Example - From Beginner To Ace
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
What Could the Inverse Sine Be?
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
The Inverse Cosine and Inverse Tangent Functions (Step-by-Step)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
Trigonometric Functions of Any Angle (Including Reference Angles)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
Trig Graphs (Vertical Transformations)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
Trig Graphs (Horizontal Transformations)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
Graphs of Sine and Cosine Functions (Amplitude, Period, and Phase Shift)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
Graphs of Tangent and Cotangent Functions (Including Transformations)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
Graphs of Secant and Cosecant Functions (Including Transformations)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
Graphing Trig Functions (Using Transformations)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
Graphing Trig Functions (Phase Shift)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
Graphing Trig Functions All You Need to Know
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
The Unit Circle With Special Angles (Constructing the Unit Circle)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
Divisibility and the Division Algorithm (Beautiful and Useful)
Dave A. Smith, Nov 11, 2022
Divisibility in the Integers (Step-By-Step Tutorials for Number Theory)
Row-Echelon Form and Gaussian Elimination (Step-by-Step)
Dave A. Smith, Nov 11, 2022
Systems of Linear Equations (In-Depth Tutorials for Linear Algebra)
Two Distinct Non-parallel Lines Have a Unique Point in Common
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
An Introduction to Sequences For Calculus Students In 9 Fun Examples
Dave A. Smith, Nov 15, 2022
Infinite Sequences and Series (Step-by-Step Tutorials for Calculus)
Radians and Degrees Explained (Step-by-Step)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
Right Angle Trigonometry (Trigonometric Functions of Acute Angles)
Dave A. Smith, Nov 15, 2022
Trigonometry is Fun (Step-by-step Tutorials for Beginners)
What Is Incidence Geometry? (and What Do We Need?)
Dave A. Smith, Nov 15, 2022
Incidence Geometry (Tutorials with Step-by-Step Proofs)
The Algebraic and Order Properties of the Real Numbers
Dave A. Smith, Nov 15, 2022
Real Analysis for Undergraduates (Complete In-Depth Tutorials)
How to Find the Area of a Surface of Revolution (Explained)
Dave A. Smith, Nov 11, 2022
Applications of Integration (Complete In-Depth Tutorials For Calculus)
The Arc Length of a Smooth Curve (in Detail)
Dave A. Smith, Nov 11, 2022
Applications of Integration (Complete In-Depth Tutorials For Calculus)
The Average Value of A Function On a Closed Interval (In Detail)
Dave A. Smith, Nov 11, 2022
Applications of Integration (Complete In-Depth Tutorials For Calculus)
How To Find Volumes Using the Shell Method (in Full)
Dave A. Smith, Nov 11, 2022
Applications of Integration (Complete In-Depth Tutorials For Calculus)
Find Volumes Using the The Washer Method (Step by Step)
Dave A. Smith, Nov 11, 2022
Applications of Integration (Complete In-Depth Tutorials For Calculus)
The Disk Method Explained (Using Python)
Dave A. Smith, Nov 11, 2022
Applications of Integration (Complete In-Depth Tutorials For Calculus)
What Are Inverse Functions? (and How to Verify Step-by-Step)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
One-to-One Functions (and the Horizontal Line Test)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Graphing an Inverse Function (by Hand and by Python)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Finding Inverse Functions (Algebraically Step-by-Step)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Composition of Functions (With Examples and Why It's Important)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Arithmetic Combinations of Functions (Add, Subtract, Multiply and Divide)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Using Transformations to Graph Functions (Shifts, Reflections, Scalings)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Using Transformations to Graph Functions (Using Python)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Transformations of Functions (and Their Graphs)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Parent Functions (and Their Transformations)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
What Are Even and Odd Functions (and Why Is This Useful?)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Introduction to the Average Rate of Change (Must Know for Calculus)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
The Difference Quotient (Find It and Use It)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Approximating the Zeros of a Function (Using Python, It's Very Easy)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Approximating a Relative Extrema (Using Python, It's Very Easy)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
What About the Range of a Function? (Sometimes Forgotten)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Introduction to Relative Minimum and Relative Maximum (What's the Point?)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Introduction to Increasing and Decreasing Functions (According to Who?)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
The Vertical Line Test for Functions (And Why It's So Useful)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Finding the Zeros of a Function (Zeros or Roots?)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Finding the Domain and Range of a Function (The Greedy Approach)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
What Are Piecewise Defined Functions? (Lots of Examples)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Intro to Functions (Guided Notes)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Graphing Lines and Circles (Using Python)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Using the Distance Formula (The EASY Way)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Examples Using The Division Algorithm (Useful)
Dave A. Smith, Nov 11, 2022
Divisibility in the Integers (Step-By-Step Tutorials for Number Theory)
The Division Algorithm (Step-By-Step Tutorial)
Dave A. Smith, Nov 11, 2022
Divisibility in the Integers (Step-By-Step Tutorials for Number Theory)
Elementary Row Operations (Remarkable Ideas)
Dave A. Smith, Nov 11, 2022
Systems of Linear Equations (In-Depth Tutorials for Linear Algebra)
How To Construct Truth Tables (Using Python)
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
How To Plot Points in the Cartesian Plane (The EASY Way)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Prove a Set of Connectives Is Functionally Complete
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
The Disk Method Around a Vertical Axis (Useful)
Dave A. Smith, Nov 11, 2022
Applications of Integration (Complete In-Depth Tutorials For Calculus)
The Disk Method Around a Horizontal Axis (Simplified)
Dave A. Smith, Nov 11, 2022
Applications of Integration (Complete In-Depth Tutorials For Calculus)
How To Use Modus Ponens and the Substitution Rule
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
Standard Form of the Equation of a Circle (Fundamentals)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Sketching the Graph of a Line (Multiple Strategies)
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Testing for Symmetry the Graph of an Equation
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Understanding the Contrapositive, Converse, and Inverse
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
What is an Augmented Matrix? (Informative)
Dave A. Smith, Nov 11, 2022
Systems of Linear Equations (In-Depth Tutorials for Linear Algebra)
Divisibility in the Integers (Useful Lemmas)
Dave A. Smith, Nov 11, 2022
Divisibility in the Integers (Step-By-Step Tutorials for Number Theory)
Finding the Extrema Using the Extreme Value Theorem
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Finding the Derivative of an Inverse Function (Examples)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Area Between Curves Vertical vs Horizontal (Explained)
Dave A. Smith, Nov 11, 2022
Applications of Integration (Complete In-Depth Tutorials For Calculus)
Finding the Intercepts of a Graph by Example
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Understanding Tautologies, Contradictions, and Contingencies
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
The Pythagorean Theorem and the Distance Formula Explained
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
Constructing Truth Tables (Helpful Step by Step Tutorial)
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
Definition of Divisibility (and Why We Need It)
Dave A. Smith, Nov 11, 2022
Divisibility in the Integers (Step-By-Step Tutorials for Number Theory)
Introduction to Systems of Linear Equations (MUST SEE)
Dave A. Smith, Nov 11, 2022
Systems of Linear Equations (In-Depth Tutorials for Linear Algebra)
Find the Area of a Region Between Two Curves Using Integration
Dave A. Smith, Nov 11, 2022
Applications of Integration (Complete In-Depth Tutorials For Calculus)
How To Plot Points in the Cartesian Plane the RIGHT Way
Dave A. Smith, Nov 15, 2022
Functions and Their Graphs (Step-by-Step Tutorials for Precalculus)
7 Logical Connectives That You MUST Master
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
The Fundamental Theorem of Calculus (Examples and Theory)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Definite Integrals and Riemann Sums (Limits To Find Area)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Using Integration by Substitution (by Example)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
What Are Indefinite Integrals (What are Antiderivatives?)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
What Are The 7 Indeterminate Forms? (L’hopital’s Rule)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Applied Optimization Problems (Procedures and Examples)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Concavity & Curve Sketching (Graphing Using Derivatives)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Horizontal and Vertical Asymptotes (Limits with Infinity)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Using the First Derivative Test: Finding Relative Extrema
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
How Do You Use the Mean Value Theorem? (Rolle’s Theorem)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
The Steps Involved in a Related Rates Problem (Implicit)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
How To Use The Tangent Line Approximation (by Example)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Implicit Differentiation (and Logarithmic) (Step by Step)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Using the Chain Rule To Find Derivatives (Many Examples)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
The (Limit Definition) of Derivative (Differentiation)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Using the Limit Definition (Precise Definition of Limit)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
What are the Conditions for a Function To Be Continuous?
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
How to Find the Limit (Techniques for Finding Limits)
Dave A. Smith, Nov 11, 2022
Calculus 1 (Explore, Discover, Learn) Series
Exercises on Mathematical Induction (10 MUST SEE)
Dave A. Smith, Nov 11, 2022
Mathematical Induction (The Complete Step-By-Step Guide)
The Mathematical Induction Equivalence (For Beginners)
Dave A. Smith, Nov 11, 2022
Mathematical Induction (The Complete Step-By-Step Guide)
The Strong Form of Induction (with Examples)
Dave A. Smith, Nov 11, 2022
Mathematical Induction (The Complete Step-By-Step Guide)
Arithmetic and Geometric Progressions (Proof of Formulas by Induction)
Dave A. Smith, Nov 11, 2022
Mathematical Induction (The Complete Step-By-Step Guide)
5 Examples Using Mathematical Induction (Worth Seeing)
Dave A. Smith, Nov 11, 2022
Mathematical Induction (The Complete Step-By-Step Guide)
Induction Principles (Basis Step Required)
Dave A. Smith, Nov 11, 2022
Mathematical Induction (The Complete Step-By-Step Guide)
The Well-Ordering Axiom (Principle or Theorem?)
Dave A. Smith, Nov 11, 2022
Mathematical Induction (The Complete Step-By-Step Guide)
First Examples Using Mathematical Induction (MUST SEE)
Dave A. Smith, Nov 11, 2022
Mathematical Induction (The Complete Step-By-Step Guide)
Find the Area Between Two Curves (Using Python)
Dave A. Smith, Nov 11, 2022
Applications of Integration (Complete In-Depth Tutorials For Calculus)
Proof By Contrapositive (What Is It And When To Use It)
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
Proof By Cases (What Is It And When To Use It)
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
Indirect Proof (What Is It And When To Use It)
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
Valid Arguments (Informative and Useful)
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
Inference Rules (Fundamentals Explained)
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
Direct Proof (What Is It And When To Use It)
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
Types of Quantifiers (and How to Use Them)
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
Multiple Quantifiers (How to Combine Quantifiers)
Dave A. Smith, Nov 14, 2022
Logic and Mathematical Proof (In-Depth Tutorials for Beginners)
Introduction to Mathematical Induction (Made Easy With Lots of Examples)
Dave A. Smith, Nov 11, 2022
Mathematical Induction (The Complete Step-By-Step Guide)