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I started my second year a couple weeks ago. At the moment I'm most interested in group theory which we started last year. In a few months we'll be doing a course which includes rings and modules which I'm looking forward to. We did a course on metric and topological spaces last year which was pretty cool.
What about you? I'd love some recommendations if you're in 3rd or 4th year
I've finished my undergraduate studies, which were almost exclusively pure in the third/fourth year!
I started my second year a couple weeks ago. At the moment I'm most interested in group theory which we started last year. In a few months we'll be doing a course which includes rings and modules which I'm looking forward to. We did a course on metric and topological spaces last year which was pretty cool.
What about you? I'd love some recommendations if you're in 3rd or 4th year
It's amazing that you took metric and topological spaces in your first year. I think Group theory is beautiful. It was one of the first course that made me realise how beautiful maths can be (and there's more to mathematical beauty than in the sense of, say, Euler's identity). I think you enjoyed the same courses that I enjoyed, so I'll just tell what books or material I found interesting/helpful!
Algebra - Thomas Hungerford: This book is beautifully written and is mostly intended as a second course in algebra. The best time to read will be concurrently with your rings and modules course or perhaps after to fully appreciate its generality. I'd personally stop after reading chapters I-IV and move to Field and Galois Theory - Patrick Morandi - since it treats field/galois theory with much better clarity and sophistication (make no mistake about it, Hungerford's book is excellent, and still better than all other algebra books - it's just that I didn't like his treatment of field theory and galois theory personally) -- you can later return to finish chapters VII-IX.
Classical Introduction Modern Number Theory - Ireland & Rosen: Now this book flows like poetry! It could be the best book ever written about mathematics. Period. The first eleven chapters require almost nothing (well the definition of things like principal ideal domain, which it defines anyway). It ends up proving quadratic/biquadratic/cubic reciprocity so many times that one of the exercises is along the lines of count the number of proofs of quadratic reciprocity given so far and give another one! Caution, though - it may turn you into a number theorist! In the end it introduces you to algebraic and analytic number theory!
After these, things open up. In my opinion, all things algebraic are beautiful, so the choices are endless! These books are expensive, though, so I'd always get them from university library or pirate them. But let me mention one last book, but with caveat that it's very challenging! I mean it makes the Rudins and Langs that people always complain about look like babies!
Fundamentals of General Topology: Problems and Exercises - A.V. Arkhangel'skii, V.I. Ponomarev It doesn't require a lot of prior knowledge - what you covered in metric/topological spaces courses would be enough, but it covers so much more than any book on general/point set topology covers (many of which are a bit outdated unlike this one, but one can use them as companion to this). Each chapter introduces some ideas then gives you tons of problems which can be solved using these ideas in novel and surprising ways! Many of the problems are very hard, but the book provides solutions to all of them at end of each chapter (well, apart from some that are actually open problems!). At the end of this, you or what's left of you
will be able to read current research in general topology! Well, it was written for the School of Soviet Mathematics who basically owned this field and you know what they say! In Soviet Russia, you don't study topology... topology studies you! 
Gojo Satoru
Staff Member
Can you help a brother out? I just want to know how they went from 3.3=log(I/Io) to 10^3.3=(I/Io)
Help a brother out ? I thought you were a girl
Anyways, there is a formula Y = Log base a * X. So when they say 3.3 = Log(1/10) all you do is use change of base formula which would be from Y = Log base a * X --> a^Y = x.
Therefore, your final solution will be 10^3.3 = 1/10 since 10 is the base of Log by default.
Feel free to ask more questions.
Gojo Satoru
Staff Member
I am a girl lmao i just say that a lotHelp a brother out ? I thought you were a girl
Anyways, there is a formula Y = Log base a * X. So when they say 3.3 = Log(1/10) all you do is use change of base formula which would be from Y = Log base a * X --> a^Y = x.
Therefore, your final solution will be 10^3.3 = 1/10 since 10 is the base of Log by default.
Feel free to ask more questions.
I don't understand what my teacher did here too
All your teacher did was move 80 from left hand side to right hand side and he just computed the equation on the Right hand side, so i'm guessing when you try punching it into your calculator it doesn't show the correct answer but try 10 * log (63) + 80. Should give you 97.99 which is approximately 98
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Gojo Satoru
Staff Member
But what about the variable that the 63 is being divided by?
What variable? log(63/1) no? Regardless just give it a shot and try to compute it, you will get the final answer.
Gojo Satoru
Staff Member
The carbon you labelled 7 has a hydroxyl, hydrogen and ch3 attached to it , meaning the longest chain has 8 carbon atoms. The hydroxyl group is on the second carbon atom and the methyl group is on the 4 carbon atom.View attachment 46863 is anyone knowledgeable in organic chemistry? I'm having troubles with 70 c) the answer booklet says it's 4-methyloctan-2-ol but I got 2,4-dimethylheptan-1-ol.
A methyl on the end means the backbone has one more ch3. You Could rotate the carbon you labelled 7 , here’s a pic of it helps.
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