Abstract Algebra Course, Lecture 1: Introduction to Groups, Modular Arithmetic, Sets, & Functions

(0:00) Welcome and syllabus.
(8:33) What is this class about? (Groups, Rings, & Fields).
(26:18) Algebraic properties of the natural numbers, whole numbers, integers, rationals, reals, and complexes.
(45:22) Modular Arithmetic ("Clock Arithmetic").
(58:12) Basics of naive set theory.
(1:05:25) Introduction to functions.

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Bill Kinney, Bethel University mathematics department

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[essadababneh]

Oh my God! You finally uploaded videos on abstract algebra. I love your method of teaching. You are an amazing teacher. I can't wait until you upload all the lectures so that I can watch them in my free time.

[minafathy]

A humble teacher with wide area of knowledge, thanks

[GrahamCrannell]

good lord... abstract algebra at 7:40am? Congrats not only to the students, but also to you haha.

[wyattlawsonskala]

Thank you for this these lectures offered the perfect insight to refresh myself on the topic to get over a road block in my reserch

[alute]

"I have goals, but don't want them to override your understanding "
I believe, Professor Kinney, that this sentence should be your thesis statement you should make for your life time goal, As a teacher for us; I hope you'd be wearing it proudly on your sleeve
Union implies could be both
Is inclusive or no exclusive or

[JagjitSingh-ykmh]

After following and leaving 2-3 lecture series ... switching among 4-5 textbooks I’ve found your lectures.
Gallian and you are a perfect match for this course.
Thank you 🙏

[imantawfiq]

It's an amazing lecture. You are the perfect teacher. I’m student in faculty of education mathematics department. I hope one day I'll be present at your lecture.

[rhysgriffiths]

I’m 12 and I went through pre calc, alg 1, 2, some of calculus 1 and now I know this and the reason why I am learning this is to go onto modular functions thank you so much

[adityaekbote]

It has been 3 years since you uploaded but these are the best I can find on the whole of internet I am high schooler and a aspiring mathematician who is deeply interested in mathematics and I am glad I found this channel I was looking for some video lectures on abstract algebra which I might understand ( education system here sucks ) also does this cover the whole year of abstract algebra course?

[ปาริชาติแซ่ย่าง-คฝ]

Still interested in maths after school 20 years ago

[smarthumanism]

Wow, a great lecture!!! I really appreciate your teaching and passion. You're not only brilliant but also passionate and inspiring. Thank you very much.

[ryanciminski]

Absolutely amazing lecture. Amazing. You just took so much stress off of me. I have a midterm coming up on Thursday and have been so stressed out as my Prof makes everything so complicated and wonky for things that can be easily understandable, which is what you do. Thank you!

[niallransford]

this is super helpful just starting to learn Galois theory really appreciate you uploading this

[onurkpolat]

Dear Professor Kinney, thank you for the lecture it was amazing! I would be grateful if you would post some exercises that we, general public could access. Thank you very very much.

[waverly]

Thanks for these lectures. When did linear algebra become so important ? I was watching Gilbert Strang's MIT lectures and he said determinants used to be what you studied in linear algebra but now determinants is just one neat corner of the subject. Another prof on you tube said you cannot learn enough linear algebra.

[melchiortod]

Really nice lecture, thank you. Am i the only one confused though about the religious talk? Is that a commun thing in the united states? Here at epfl a teacher would instantly stop teaching if he did something like that. But besides from that very nice introduction, and not to hard on the students. Smells of success

[brandonfox]

Hi, again! Looking back at this lecture, I actually don't like that you included "closure" as a property/axiom, since when you write that N^+ (that is, the set of natural numbers under the binary operation of addition), you're already implying that natural numbers are closed under addition because obviously, in this case, any natural number plus any natural number gives us a natural number. Also, the definition of groups already has the "closure" part in it already, so you don't need to list it as a property/axiom.

[katth]

Hello! When you explained operation on sets, why you didn’t arrange omega? I mean like omega belongs to R or something like that

[prakashchaurasiap]

(45:22) Modular Arithmetic ("Clock Arithmetic").

[qbtc]

I have just finished Professor Strang's Linear Algebra course and want to go on to Abstract Algebra and Real Analysis. Is it better to do Abstract Algebra first or Analysis? I got my BS in physics 20 years ago and want to learn all the math that I missed out on. Thanks for sharing these great lectures.