MATH 558 | Introductory Modern Algebra Professor Emily Witt August 25, 2020
Introductions
About your instructor 1
About your instructor 2
About your instructor 3
About your instructor My mathematical research is in the area of commutative algebra . 4
Expectations: In class Wear a mask in class at all times, and properly social distance. Stay off cell phones and computers. Stay awake. Take notes, or otherwise actively follow the discussion. Be willing to volunteer answers when asked. Interrupt if you have questions or comments. Be respectful to your peers. 5
Expectations: Outside of class Closely follow the Course Digest. Start the tasks in the Course Digest as soon as possible. Memorize definitions as soon as possible. Memorize statements of theorems as soon as possible. Make notecards to help with memorization, if necessary. Produce examples and non-examples to help understand definitions. Be responsive, and contribute, during online group assignments. Be diligent and work hard. 6
Modern Algebra
Modern Algebra “Mathematics is the queen of the sciences and number theory is the queen of mathematics.” –Carl Friedrich Gauss Generalizing the notion of solving equations. “Modern” or “Abstract” Algebra. Groups, rings, and fields. Applications to machine learning, genomics, cryptography, etc. 7
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