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Doctor Albert’s Chalkboard

Doctor Albert’s Chalkboard

Expanding your knowledge and love of mathematics.

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Tag: Mathematics

Blogs

YouTube Classes

March 19, 2020 Dr. Justin Albert

Due to covid-19, all my classes will be streamed on YouTube the rest of the semester. Read here to find out more about how to join!

Tagged Discord, Math, Mathematics, online classes, twitch, YouTubeLeave a comment
algebraic structures, Blogs

Field Generated by 1

February 19, 2020 Dr. Justin Albert

We find the smallest field containing the number 1 when using the usual addition and multiplication of real numbers.

Tagged abstract algebra, field, generator, Math, Mathematics, ringLeave a comment
algebraic structures, Blogs

Integral Domain of Integers

January 30, 2020January 30, 2020 Dr. Justin Albert

We show that the integers modulo any prime forms an integral domain under addition and multiplication modulo p.

Tagged congruence, integral domain, Math, Mathematics, modulo, ringLeave a comment
algebraic structures, Blogs

A Ring of Matrices

January 27, 2020February 6, 2020 Dr. Justin Albert

We show, step-by-step, that the set of all 2 x 2 matrices with real entries forms a ring under addition and multiplication.

Tagged abstract algebra, associative, commutative, Group, Math, Mathematics, matrices, monoid, ring, semigroupLeave a comment
algebraic structures, Blogs

Representations of Cyclic Groups

January 22, 2020April 8, 2020 Dr. Justin Albert

We show that every cyclic group is isomorphic to either the set of integers or the set of integers mod some integer under addition.

Tagged abstract algebra, cyclic group, Groups, isomorphism, Math, Mathematics, representation theory1 Comment

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Top Posts

  • How many ways can you get a straight or a flush in poker?
    How many ways can you get a straight or a flush in poker?
  • Area of a triangle: Integration
    Area of a triangle: Integration
  • Proof By Contradiction: There are no integer solutions to 14x+6y=1.
    Proof By Contradiction: There are no integer solutions to 14x+6y=1.
  • Tangents to Parametric Equations
    Tangents to Parametric Equations
  • Congruence Modulo n
    Congruence Modulo n
  • Composition of Mappings on a Set
    Composition of Mappings on a Set