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Studying Mathematics Thread
#34
RE: Studying Mathematics Thread
IMO, when studying math, it is extremely important to not get discouraged when encountering a challenging concept, proof, definition, theorem, etc.  A couple of days ago, I encountered a proof dealing with the power series and the concept of the radius of convergence.  When I got to sentence 3, I was unsure how the author drew a particular conclusion, and as a result, I got stuck and ultimately decided to take a break from it.  However, today I was thinking more clearly and realized that if I took the negation of a particular definition (in this case, the definition of a bounded sequence), then the sentence made much more sense.  Thus, difficult concepts are a part of mathematics: sometimes I'm fortunate enough to be able to wrap my head around them; however, there are times when it is necessary to let some difficult concepts go and make a note of them, so that you don't waste time staring into space when you could be  learning new/important material that comes more easily to you (sometimes covering new material may provide more insight about the challenging concept).  Hence, you can always come back to the difficult stuff later or ask someone who knows more about math for help, especially if the concepts are fundamental to successfully understanding the topic one is studying; there's no shame in asking for help, as it is part of the learning process.

Also, IMO, when studying higher level mathematics, it is crucial that one has a solid understanding of mathematical proofs.  IMO, when taking a course in mathematical proofs for the first time, it is important that students do the following: give themselves ample time to digest the various proof-writing concepts, especially the basic proof-writing techniques; be willing to practice and work various proof exercises, so that they will gain first-hand experience navigating the proof-writing process (this often involves at least a draft of one's thought processes which is eventually harmonized into a coherent final proof); learn how to read condensed proofs via spotting key words that give away basic proof-writing techniques and being able to fill in the missing details via considering how one would get from A to B via theorems, definitions, previous knowledge, etc.; when writing final/condensed proofs, be sure to keep any clarifying notes (especially the analysis of proof, which IMO, is where the proof is actually explained and understood) that explain the fine details of a proof, because these notes will save you the time of having to figure things out again, especially if you haven't reviewed the proof for some time (days, weeks, months) and are somewhat rusty with the concepts, definitions, theorems, etc., that are involved in the proof.  IMO, reading the condensed proof of another author makes one appreciate the value of including an analysis of proof with the final condensed proof.











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Messages In This Thread
Studying Mathematics Thread - by Grandizer - February 28, 2018 at 11:22 am
RE: Studying Mathematics Thread - by Silver - February 28, 2018 at 11:31 am
RE: Studying Mathematics Thread - by Tiberius - February 28, 2018 at 11:36 am
RE: Studying Mathematics Thread - by Whateverist - February 28, 2018 at 3:58 pm
RE: Studying Mathematics Thread - by polymath257 - February 28, 2018 at 11:45 am
RE: Studying Mathematics Thread - by robvalue - February 28, 2018 at 1:21 pm
RE: Studying Mathematics Thread - by polymath257 - February 28, 2018 at 2:08 pm
RE: Studying Mathematics Thread - by Edwardo Piet - February 28, 2018 at 2:10 pm
RE: Studying Mathematics Thread - by polymath257 - February 28, 2018 at 2:35 pm
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - February 28, 2018 at 8:55 pm
RE: Studying Mathematics Thread - by Grandizer - February 28, 2018 at 9:00 pm
RE: Studying Mathematics Thread - by Edwardo Piet - February 28, 2018 at 9:02 pm
RE: Studying Mathematics Thread - by Fireball - February 28, 2018 at 3:53 pm
RE: Studying Mathematics Thread - by Alexmahone - February 28, 2018 at 3:54 pm
RE: Studying Mathematics Thread - by LadyForCamus - February 28, 2018 at 10:22 pm
RE: Studying Mathematics Thread - by Grandizer - February 28, 2018 at 10:59 pm
RE: Studying Mathematics Thread - by polymath257 - March 3, 2018 at 7:12 pm
RE: Studying Mathematics Thread - by Grandizer - March 3, 2018 at 7:52 pm
RE: Studying Mathematics Thread - by polymath257 - March 3, 2018 at 9:00 pm
RE: Studying Mathematics Thread - by robvalue - March 4, 2018 at 7:12 am
RE: Studying Mathematics Thread - by Grandizer - March 6, 2018 at 7:58 am
RE: Studying Mathematics Thread - by polymath257 - March 6, 2018 at 9:21 am
RE: Studying Mathematics Thread - by robvalue - March 7, 2018 at 1:51 am
RE: Studying Mathematics Thread - by polymath257 - March 7, 2018 at 8:19 am
RE: Studying Mathematics Thread - by Grandizer - March 7, 2018 at 8:41 am
RE: Studying Mathematics Thread - by robvalue - March 7, 2018 at 8:48 am
RE: Studying Mathematics Thread - by polymath257 - March 7, 2018 at 8:49 am
RE: Studying Mathematics Thread - by robvalue - March 7, 2018 at 8:30 am
RE: Studying Mathematics Thread - by polymath257 - March 7, 2018 at 8:42 am
RE: Studying Mathematics Thread - by robvalue - March 7, 2018 at 8:53 am
RE: Studying Mathematics Thread - by polymath257 - March 7, 2018 at 9:01 am
RE: Studying Mathematics Thread - by robvalue - March 7, 2018 at 10:19 am
RE: Studying Mathematics Thread - by polymath257 - March 7, 2018 at 10:43 am
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - March 8, 2018 at 1:54 am
RE: Studying Mathematics Thread - by robvalue - March 8, 2018 at 2:46 am
RE: Studying Mathematics Thread - by Grandizer - March 8, 2018 at 3:39 am
RE: Studying Mathematics Thread - by robvalue - March 8, 2018 at 3:49 am
RE: Studying Mathematics Thread - by Grandizer - March 8, 2018 at 3:53 am
RE: Studying Mathematics Thread - by polymath257 - March 8, 2018 at 10:47 am
RE: Studying Mathematics Thread - by Edwardo Piet - April 20, 2018 at 10:22 am
RE: Studying Mathematics Thread - by Grandizer - April 20, 2018 at 11:10 am
RE: Studying Mathematics Thread - by Grandizer - April 20, 2018 at 10:39 pm
RE: Studying Mathematics Thread - by polymath257 - April 21, 2018 at 10:06 am
RE: Studying Mathematics Thread - by robvalue - March 8, 2018 at 4:00 am
RE: Studying Mathematics Thread - by Grandizer - March 8, 2018 at 4:11 am
RE: Studying Mathematics Thread - by Grandizer - March 8, 2018 at 8:43 am
RE: Studying Mathematics Thread - by robvalue - March 8, 2018 at 9:48 am
RE: Studying Mathematics Thread - by Grandizer - March 15, 2018 at 1:49 am
RE: Studying Mathematics Thread - by polymath257 - March 18, 2018 at 10:43 pm
RE: Studying Mathematics Thread - by Grandizer - March 19, 2018 at 9:11 am
RE: Studying Mathematics Thread - by polymath257 - March 19, 2018 at 9:32 pm
RE: Studying Mathematics Thread - by polymath257 - March 22, 2018 at 9:34 am
RE: Studying Mathematics Thread - by Grandizer - March 22, 2018 at 10:06 am
RE: Studying Mathematics Thread - by Grandizer - March 22, 2018 at 9:58 pm
RE: Studying Mathematics Thread - by polymath257 - March 23, 2018 at 7:44 am
RE: Studying Mathematics Thread - by Grandizer - March 24, 2018 at 8:45 am
RE: Studying Mathematics Thread - by polymath257 - March 24, 2018 at 9:52 am
RE: Studying Mathematics Thread - by Grandizer - April 4, 2018 at 10:35 pm
RE: Studying Mathematics Thread - by polymath257 - April 5, 2018 at 7:41 am
RE: Studying Mathematics Thread - by robvalue - April 5, 2018 at 8:48 am
RE: Studying Mathematics Thread - by polymath257 - April 5, 2018 at 9:01 am
RE: Studying Mathematics Thread - by Grandizer - April 5, 2018 at 9:03 am
RE: Studying Mathematics Thread - by Grandizer - April 5, 2018 at 8:25 pm
RE: Studying Mathematics Thread - by robvalue - April 6, 2018 at 2:18 am
RE: Studying Mathematics Thread - by Grandizer - April 6, 2018 at 2:58 am
RE: Studying Mathematics Thread - by robvalue - April 6, 2018 at 4:16 am
RE: Studying Mathematics Thread - by Grandizer - April 6, 2018 at 4:22 am
RE: Studying Mathematics Thread - by polymath257 - April 6, 2018 at 7:53 am
RE: Studying Mathematics Thread - by robvalue - April 9, 2018 at 12:58 pm
RE: Studying Mathematics Thread - by Grandizer - April 9, 2018 at 11:46 am
RE: Studying Mathematics Thread - by Silver - April 9, 2018 at 1:01 pm
RE: Studying Mathematics Thread - by robvalue - April 9, 2018 at 1:09 pm
RE: Studying Mathematics Thread - by polymath257 - April 9, 2018 at 1:20 pm
RE: Studying Mathematics Thread - by robvalue - April 9, 2018 at 1:22 pm
RE: Studying Mathematics Thread - by Grandizer - April 14, 2018 at 2:07 am
RE: Studying Mathematics Thread - by polymath257 - April 14, 2018 at 10:24 am
RE: Studying Mathematics Thread - by robvalue - April 14, 2018 at 10:41 am
RE: Studying Mathematics Thread - by Grandizer - April 15, 2018 at 5:18 am
RE: Studying Mathematics Thread - by Jarrey - April 15, 2018 at 7:12 am
RE: Studying Mathematics Thread - by robvalue - April 15, 2018 at 7:53 am
RE: Studying Mathematics Thread - by Grandizer - April 15, 2018 at 9:21 am
RE: Studying Mathematics Thread - by polymath257 - April 15, 2018 at 10:26 am
RE: Studying Mathematics Thread - by Grandizer - April 19, 2018 at 10:39 pm
RE: Studying Mathematics Thread - by robvalue - April 21, 2018 at 3:44 am
RE: Studying Mathematics Thread - by Edwardo Piet - April 21, 2018 at 10:09 am
RE: Studying Mathematics Thread - by Grandizer - April 23, 2018 at 5:51 pm
RE: Studying Mathematics Thread - by polymath257 - April 23, 2018 at 10:09 pm
RE: Studying Mathematics Thread - by Divinity - April 23, 2018 at 7:19 pm
RE: Studying Mathematics Thread - by Grandizer - April 23, 2018 at 8:32 pm
RE: Studying Mathematics Thread - by Divinity - April 23, 2018 at 10:45 pm
RE: Studying Mathematics Thread - by Grandizer - April 24, 2018 at 2:18 am
RE: Studying Mathematics Thread - by polymath257 - April 24, 2018 at 8:13 am
RE: Studying Mathematics Thread - by Fireball - April 23, 2018 at 8:20 pm
RE: Studying Mathematics Thread - by Grandizer - April 24, 2018 at 4:43 am
RE: Studying Mathematics Thread - by polymath257 - April 24, 2018 at 8:24 am
RE: Studying Mathematics Thread - by robvalue - April 24, 2018 at 5:09 am
RE: Studying Mathematics Thread - by Grandizer - April 24, 2018 at 8:18 am
RE: Studying Mathematics Thread - by polymath257 - April 24, 2018 at 11:24 am
RE: Studying Mathematics Thread - by polymath257 - April 26, 2018 at 7:48 am
RE: Studying Mathematics Thread - by Grandizer - April 27, 2018 at 7:19 pm
RE: Studying Mathematics Thread - by polymath257 - April 27, 2018 at 8:53 pm
RE: Studying Mathematics Thread - by Grandizer - April 28, 2018 at 1:41 am
RE: Studying Mathematics Thread - by polymath257 - April 28, 2018 at 9:51 am
RE: Studying Mathematics Thread - by Grandizer - April 28, 2018 at 11:35 pm
RE: Studying Mathematics Thread - by polymath257 - April 29, 2018 at 9:00 am
RE: Studying Mathematics Thread - by Grandizer - April 30, 2018 at 9:48 am
RE: Studying Mathematics Thread - by polymath257 - April 30, 2018 at 1:15 pm
RE: Studying Mathematics Thread - by Grandizer - April 30, 2018 at 7:42 pm
RE: Studying Mathematics Thread - by polymath257 - April 30, 2018 at 8:09 pm
RE: Studying Mathematics Thread - by Grandizer - May 1, 2018 at 2:19 am
RE: Studying Mathematics Thread - by Grandizer - April 28, 2018 at 9:29 am
RE: Studying Mathematics Thread - by polymath257 - May 1, 2018 at 7:55 am
RE: Studying Mathematics Thread - by Grandizer - May 1, 2018 at 7:59 am
RE: Studying Mathematics Thread - by Fireball - May 1, 2018 at 11:43 pm
RE: Studying Mathematics Thread - by Grandizer - May 2, 2018 at 6:35 am
RE: Studying Mathematics Thread - by Fireball - May 2, 2018 at 11:43 am
RE: Studying Mathematics Thread - by polymath257 - May 4, 2018 at 8:14 am
RE: Studying Mathematics Thread - by Fireball - June 15, 2018 at 12:35 pm
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - June 15, 2018 at 11:45 am
RE: Studying Mathematics Thread - by polymath257 - June 15, 2018 at 3:46 pm
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - July 6, 2018 at 3:23 am
RE: Studying Mathematics Thread - by polymath257 - July 6, 2018 at 8:42 pm
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - July 17, 2018 at 2:02 am
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - September 27, 2018 at 1:59 am
RE: Studying Mathematics Thread - by The Valkyrie - September 27, 2018 at 2:01 am
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - September 27, 2018 at 2:10 am
RE: Studying Mathematics Thread - by polymath257 - September 27, 2018 at 8:07 am
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - September 27, 2018 at 7:13 pm
RE: Studying Mathematics Thread - by Grandizer - September 27, 2018 at 7:20 pm
RE: Studying Mathematics Thread - by polymath257 - September 27, 2018 at 9:06 pm
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - September 28, 2018 at 5:34 pm
RE: Studying Mathematics Thread - by Aliza - September 28, 2018 at 6:57 pm
RE: Studying Mathematics Thread - by polymath257 - September 29, 2018 at 9:16 am
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - September 29, 2018 at 10:50 am
RE: Studying Mathematics Thread - by polymath257 - September 29, 2018 at 6:02 pm
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - September 29, 2018 at 10:01 pm
RE: Studying Mathematics Thread - by Aliza - September 30, 2018 at 2:40 pm
RE: Studying Mathematics Thread - by Aliza - September 29, 2018 at 6:21 pm
RE: Studying Mathematics Thread - by Tiberius - September 27, 2018 at 2:11 am
RE: Studying Mathematics Thread - by Aliza - September 27, 2018 at 2:23 am
RE: Studying Mathematics Thread - by robvalue - September 28, 2018 at 1:35 am
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - September 28, 2018 at 8:02 pm
RE: Studying Mathematics Thread - by Aliza - September 28, 2018 at 8:21 pm
RE: Studying Mathematics Thread - by Fireball - September 29, 2018 at 7:56 pm
RE: Studying Mathematics Thread - by Aliza - September 29, 2018 at 8:05 pm
RE: Studying Mathematics Thread - by Fireball - September 29, 2018 at 9:08 pm
RE: Studying Mathematics Thread - by Aliza - September 30, 2018 at 12:12 am
RE: Studying Mathematics Thread - by Fireball - September 30, 2018 at 7:56 pm
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - September 30, 2018 at 10:11 pm
RE: Studying Mathematics Thread - by Aliza - September 30, 2018 at 10:18 pm
RE: Studying Mathematics Thread - by Fireball - September 30, 2018 at 10:44 pm
RE: Studying Mathematics Thread - by polymath257 - October 1, 2018 at 8:06 am
RE: Studying Mathematics Thread - by LastPoet - October 2, 2018 at 7:40 am
RE: Studying Mathematics Thread - by polymath257 - October 2, 2018 at 7:58 am
RE: Studying Mathematics Thread - by Reltzik - October 2, 2018 at 10:49 am
RE: Studying Mathematics Thread - by Reltzik - October 2, 2018 at 10:58 am
RE: Studying Mathematics Thread - by polymath257 - October 2, 2018 at 11:34 am
RE: Studying Mathematics Thread - by Grandizer - October 2, 2018 at 11:05 am
RE: Studying Mathematics Thread - by Aliza - October 2, 2018 at 11:29 am
RE: Studying Mathematics Thread - by Grandizer - October 2, 2018 at 11:35 am
RE: Studying Mathematics Thread - by polymath257 - October 2, 2018 at 12:03 pm
RE: Studying Mathematics Thread - by Aliza - October 2, 2018 at 12:50 pm
RE: Studying Mathematics Thread - by Grandizer - October 2, 2018 at 1:23 pm
RE: Studying Mathematics Thread - by polymath257 - October 2, 2018 at 1:29 pm
RE: Studying Mathematics Thread - by Aliza - October 3, 2018 at 1:53 am
RE: Studying Mathematics Thread - by polymath257 - October 3, 2018 at 8:30 am
RE: Studying Mathematics Thread - by Fireball - October 3, 2018 at 11:30 am
RE: Studying Mathematics Thread - by polymath257 - October 3, 2018 at 12:25 pm
RE: Studying Mathematics Thread - by Fireball - October 3, 2018 at 1:03 pm
RE: Studying Mathematics Thread - by robvalue - October 1, 2018 at 1:54 am
RE: Studying Mathematics Thread - by Reltzik - October 2, 2018 at 2:51 am
RE: Studying Mathematics Thread - by Grandizer - October 5, 2018 at 1:19 pm
RE: Studying Mathematics Thread - by Fireball - October 9, 2018 at 8:03 pm
RE: Studying Mathematics Thread - by Grandizer - October 10, 2018 at 12:13 am
RE: Studying Mathematics Thread - by Aliza - October 10, 2018 at 3:10 pm
RE: Studying Mathematics Thread - by Grandizer - October 10, 2018 at 11:34 pm
RE: Studying Mathematics Thread - by Reltzik - October 11, 2018 at 12:20 am
RE: Studying Mathematics Thread - by Aliza - October 11, 2018 at 12:30 am
RE: Studying Mathematics Thread - by Reltzik - October 11, 2018 at 12:35 am
RE: Studying Mathematics Thread - by Aliza - October 11, 2018 at 12:53 am
RE: Studying Mathematics Thread - by Aliza - October 11, 2018 at 12:41 pm
RE: Studying Mathematics Thread - by Reltzik - October 11, 2018 at 2:47 pm
RE: Studying Mathematics Thread - by DodosAreDead - October 11, 2018 at 12:21 am
RE: Studying Mathematics Thread - by EgoDeath - October 9, 2018 at 4:20 pm
RE: Studying Mathematics Thread - by Reltzik - October 9, 2018 at 7:55 pm
RE: Studying Mathematics Thread - by EgoDeath - October 10, 2018 at 9:46 am
RE: Studying Mathematics Thread - by Reltzik - October 10, 2018 at 3:37 pm
RE: Studying Mathematics Thread - by EgoDeath - October 10, 2018 at 11:29 pm
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - October 10, 2018 at 12:07 am
RE: Studying Mathematics Thread - by Fireball - October 11, 2018 at 2:28 am
RE: Studying Mathematics Thread - by Aliza - October 11, 2018 at 10:08 am
RE: Studying Mathematics Thread - by Grandizer - October 11, 2018 at 7:31 pm
RE: Studying Mathematics Thread - by Fireball - October 11, 2018 at 8:34 pm
RE: Studying Mathematics Thread - by Reltzik - October 12, 2018 at 11:34 pm
RE: Studying Mathematics Thread - by Aliza - October 13, 2018 at 2:07 am
RE: Studying Mathematics Thread - by Kernel Sohcahtoa - October 13, 2018 at 6:40 pm
RE: Studying Mathematics Thread - by Fireball - October 13, 2018 at 8:15 pm
RE: Studying Mathematics Thread - by polymath257 - October 14, 2018 at 11:33 pm
RE: Studying Mathematics Thread - by Grandizer - October 27, 2018 at 11:39 am
RE: Studying Mathematics Thread - by Fireball - October 27, 2018 at 11:54 am
RE: Studying Mathematics Thread - by Aliza - October 28, 2018 at 12:23 am
RE: Studying Mathematics Thread - by Grandizer - October 28, 2018 at 7:42 pm
RE: Studying Mathematics Thread - by Silver - October 30, 2018 at 6:03 am
RE: Studying Mathematics Thread - by Aliza - October 30, 2018 at 10:55 am
RE: Studying Mathematics Thread - by Grandizer - October 31, 2018 at 10:14 am
RE: Studying Mathematics Thread - by Grandizer - November 3, 2018 at 1:15 am
RE: Studying Mathematics Thread - by Grandizer - November 3, 2018 at 6:30 am
RE: Studying Mathematics Thread - by Fireball - October 30, 2018 at 6:44 am
RE: Studying Mathematics Thread - by Jehanne - November 2, 2018 at 9:02 am
RE: Studying Mathematics Thread - by Macoleco - November 3, 2018 at 11:15 pm
RE: Studying Mathematics Thread - by polymath257 - November 4, 2018 at 9:26 am
RE: Studying Mathematics Thread - by Jehanne - November 5, 2018 at 9:55 am
RE: Studying Mathematics Thread - by polymath257 - November 5, 2018 at 1:03 pm
RE: Studying Mathematics Thread - by Jehanne - November 6, 2018 at 8:37 am
RE: Studying Mathematics Thread - by polymath257 - November 7, 2018 at 1:31 pm
RE: Studying Mathematics Thread - by Jehanne - November 7, 2018 at 3:51 pm
RE: Studying Mathematics Thread - by polymath257 - November 7, 2018 at 5:30 pm
RE: Studying Mathematics Thread - by Jehanne - November 8, 2018 at 11:34 pm
RE: Studying Mathematics Thread - by polymath257 - November 9, 2018 at 10:20 am
RE: Studying Mathematics Thread - by Silver - November 8, 2018 at 10:22 am
RE: Studying Mathematics Thread - by bennyboy - November 19, 2018 at 12:48 am
RE: Studying Mathematics Thread - by Fireball - November 19, 2018 at 1:28 am

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