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Bill K. has helped students times in
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Bill K.

I'm a mathematics professor at Bethel University, St. Paul, MN. I make a lot of math videos for YouTube, often focused on using the program Mathematica. My Ph.D. is from the University of Minnesota. My research has been in applications of Conley Index Theory, a part of dynamical systems that applies topological methods to differential equations ("continuous dynamics") and iteration of maps ("discrete dynamics"). I'm also interested in actuarial science and complex analysis education reform.


86K karma · St. Paul, Minnesota, USA
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Level 16 in Calculus Level 13 in Algebra Level 11 in Precalculus Level 8 in Trigonometry Level 8 in Statistics Level 4 in Physics Level 3 in Prealgebra Level 2 in Socratic Meta
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Activity Videos 643 Answers 1283 Edits

Algebra

  1. 1

    Properties of Real Numbers

    1. Properties of Rational Numbers
      1. Adding Fractions by Getting a Common Denominator
      2. Finding a Combined Painting Rate for Two People by Adding Fractions
      3. How Fast Can a Room be Painted if Two People Paint at Different Rates?
      4. Multiply & Add Fractions to Solve Painting Rate Probs, Use Prime Factorization to Multiply Fractions
      5. Multiplying Fractions using Prime Factorization
      6. Reducing Fractions before Multiplying, Calories for a Fraction of a Pie
      7. Calculate calories for a piece of pie cut differently than a serving size, Fraction Division
      8. Dividing Fractions by Inverting and Multiplying, Spending on Food Problem
      9. Using Division of Fractions to Determine Recipe Amounts
      10. Algebraic Properties of the Rational Numbers, illustrated with particular examples
    2. Additive Inverses and Absolute Values
      1. Intro to Number Systems, Closure, Additive Identity & Additive Inverses, Basic Applications
      2. Closure, Relating Subtraction to Addition, Commutative Property, Application to Motion along a Line
      3. Additive Identity & Inverses, Negative Numbers, Add & Subtract on the Number Line
    3. Addition of Integers
      1. Intro to Number Systems, Closure, Additive Identity & Additive Inverses, Basic Applications
      2. Closure, Relating Subtraction to Addition, Commutative Property, Application to Motion along a Line
      3. Additive Identity & Inverses, Negative Numbers, Add & Subtract on the Number Line
    4. Multiplication of Rational Numbers
      1. Multiply & Add Fractions to Solve Painting Rate Probs, Use Prime Factorization to Multiply Fractions
      2. Multiplying Fractions using Prime Factorization
      3. Reducing Fractions before Multiplying, Calories for a Fraction of a Pie
      4. Calculate calories for a piece of pie cut differently than a serving size, Fraction Division
      5. Dividing Fractions by Inverting and Multiplying, Spending on Food Problem
      6. Using Division of Fractions to Determine Recipe Amounts

Macroeconomics

  1. 1

Statistics

  1. 1
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