Abstract Algebra Exam 1 Review Problems and Solutions

[@TwistedFour]

Hello Dr. Kinney, I'm studying for my exam right now and your video helped me out a lot. I appreciate you taking your time to make this review guide for students. Thank you and have a wonderful day.

[@billkinneymath]

You're welcome! Hope you do well!

[@brandonfox9618]

For the binary operation, you needed a Cartesian product for the first part. Every unique ordered pair (a, b) in G X G gets assigned to an element a * b in G.

[@billkinneymath]

Yes. I was being a bit less formal than I probably should have been there.

[@brandonfox9618]

@@billkinneymath No problem! You do have much more experience in this than me. I am just a recent graduate from college after all.

[@JamesWeeks-j8m]

Hi Dr. Kinney, Thanks for the excellent review. I am back in college after being gone for 4 years and the first proof-based math course I am taking (outside of Intro to Proofs) is Abstract Algebra. Preparing for exam in 2 weeks so this was amazing in making sure I understood some of the fundamental concepts, problems, proofs. It has been tough learning this subject and relearning complex numbers, basic linear algebra, but so far has been a great experience in learning the basics of Abstract Algebra.

[@billkinneymath]

You're welcome! Hope the class goes well for you!

[@filipjohansen9937]

The quality of your content is phenomenal. It's quite the gift to the world

[@billkinneymath]

Thanks! That's very kind of you. So glad you find it so helpful.

[@SphereofTime]

1:00 awesome video!!!!❤❤

[@richard-1604]

Thank you very much for sharing these lectures and examples. I’m a retired IT consultant who has always enjoyed maths and did some research a long time ago. Your lectures are very clear and these examples are useful and illuminating too.

[@billkinneymath]

You're welcome! So glad they are helpful for you!

[@s1mpelness771]

Ive started college about three days ago and abstract algebra aswell, and this really helped me , thanks for what you do sir

[@billkinneymath]

You're welcome! Hope it goes well for you!

[@ronmiller1421]

You are an excellent professor in Mathematics Professor Kinney. Keep up the excellent lectures!

[@billkinneymath]

Thanks!

[@martinhawrylkiewicz2025]

Great vid! I took Abstract algebra as an undergrad a decade ago and really liked it but over the years I forgot a lot of things, so now I am starting to teach myself Abstract Algebra using a textbook by John Fraleigh (7th edition). I find it very refreshing and wonderful to be able to see abstract algebra again after all these years.

[@billkinneymath]

Thanks! Yes, it's such a beautiful subject!

[@willgreencinema]

Thank you so much. I have always enjoyed learning mathematics. You teach very well and I am very thankful for your videos! Please keep them up!!

[@billkinneymath]

You're welcome! Thanks so much for watching. I'm glad you are learning a lot.

[@PLP0321]

Wish I had this video when I was taking abstract! Thanks, Professor.

[@billkinneymath]

You're welcome!

[@eddiejennings5262]

Thank you! A great gift to math students.

[@billkinneymath]

You're welcome!

[@mathematik6016]

I love this Review Exam....help so so so much!!!!

[@billkinneymath]

Awesome! Hope your exams go well!

[@Simpuls]

Writing a comment on the things I learned in this video which I didn't know before: 1. cyclic is not equal to a group being generated by elements. For Question 9 I wasn't sure. Since D3 is in fact generated by just rotations and symmetries I thought, maybe that's the same as saying, it's cyclic, but it's not. Cyclic seems to mean, that one and only one element generates the Group.

[@billkinneymath]

You got it! Though a group can be generated by more than one element, it's just not cyclic in that case.

[@Simpuls]

@@billkinneymath I learned way more than one thing in your video, but since I watched the full thing yesterday evening, I started taking notes on my college tablet instead of comments! Will be watching the other algebra exam videos as well!

[@billkinneymath]

@@Simpuls Awesome!

[@FerreroRocher-r3f]

Thank you so much for this Sir, this is so helpful ❤

[@billkinneymath]

You're welcome! So glad it's helpful for you!

[@oldPrince22]

Well explained everything, good video!

[@billkinneymath]

Thanks!

[@filipkarkalasev]

Thank you, very clear!

[@billkinneymath]

You're welcome! Thanks for watching!

[@mzarinchang3744]

That was awesome. Thank youuuuu

[@billkinneymath]

You're welcome! Pass the word!

[@leonardomurgia4959]

10:01 Shouldn't it be ∃! Instead of ∃?

[@billkinneymath]

Uniqueness is true, but you don't need to assume it in the definition. It's something you can prove.

[@王贺煊]

thank you Mr you save my life

[@billkinneymath]

So glad to be of help!

[@joshbullis2322]

Hello Professor! I am about to take Abstract Algebra (undergrad). I have had Real Analysis and Topology already, but im still nervous about the new semester. Im also doing DiffEQ and Complex Analysis. Do you have any advice about how to manage those 3 courses in the same semester. Thanks!

[@billkinneymath]

Abstract Algebra is probably the one that is the hardest for most people. But since you've had Real Analysis and Topology already, you should be able to handle the abstraction better than most people. Your DiffEQ and Complex Analysis will probably be less abstract, but they can still be tough. Time management will be key. I've got lectures on all 3 subjects if you find them helpful. God bless!

[@joshbullis2322]

@@billkinneymath thank you for the advice! I will definitely refer to your lectures throughout the upcoming semester, thank you for creating this content!

[@billkinneymath]

@@joshbullis2322 You're welcome!

[@violettangie1560]

love it !

[@billkinneymath]

Thanks!

[@Grassmpl]

Easy as heck man