Notices
Results 1 to 10 of 10

Thread: Strong foundation's!

  1. #1 Strong foundation's! 
    Your Mama! GiantEvil's Avatar
    Join Date
    Apr 2010
    Location
    Vancouver, Wa
    Posts
    2,309
    Is there a mental exercise which has a tendency to order the mind such that the understanding and retention of mathematical concepts, symbology, and algorithmic procedure is increased?


    I was some of the mud that got to sit up and look around.
    Lucky me. Lucky mud.
    -Kurt Vonnegut Jr.-
    Cat's Cradle.
    Reply With Quote  
     

  2.  
     

  3. #2 Re: Strong foundation's! 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by GiantEvil
    Is there a mental exercise which has a tendency to order the mind such that the understanding and retention of mathematical concepts, symbology, and algorithmic procedure is increased?
    Sometimes it seems to help if one is sober.


    Reply With Quote  
     

  4. #3  
    Forum Radioactive Isotope MagiMaster's Avatar
    Join Date
    Jul 2006
    Posts
    3,440
    You might want to look up recreational mathematics. It's not an exercise, but it might increase interest, which is probably more important.
    Reply With Quote  
     

  5. #4 Re: Strong foundation's! 
    Your Mama! GiantEvil's Avatar
    Join Date
    Apr 2010
    Location
    Vancouver, Wa
    Posts
    2,309
    Quote Originally Posted by DrRocket
    Quote Originally Posted by GiantEvil
    Is there a mental exercise which has a tendency to order the mind such that the understanding and retention of mathematical concepts, symbology, and algorithmic procedure is increased?
    Sometimes it seems to help if one is sober.
    While I intentionally enjoy the occasional buzz, I am by no means a drunkard. The only substance's I have ever meet the criteria for psychological and physiological addiction to is nicotine and caffeine, and I have wholly surrendered the use of nicotine, though I suspect that addiction itself will be with me to the end of my days. I am currently drinking a cup of coffee right now.

    Now, back to my original query.
    Say one want's to learn to juggle. It is good to start with one object, preferably uniform, and not to hard or bouncy. Then one assumes a rigid posture and practices throwing the object from one hand into the other with as minimal a movement as possible. This is the basic drill for developing the fundamental skill necessary to juggling.

    I am asking for a drill that strengthens the fundamental skill's necessary to the study and understanding of pattern and order.
    As an example, while travelling, picking two points on the horizon and using them, and myself as a third point, to visualize a triangle which would close down to a line segment as my ray of travel intersects the line segment formed by the two original points?

    Or, whenever a discernable group of object's fall's within my vision, I could consider them a set, count them to discover the cardinality of the set, then group the set into subsets based on arbitrary equivalence classes?

    Perhaps to never do a one to one count of objects in a geometric arrangement, but to always deduce their number from edge count and formula?
    Quote Originally Posted by MagiMaster
    You might want to look up recreational mathematics. It's not an exercise, but it might increase interest, which is probably more important.
    Thank you MagiMaster for the suggestion, though I can confidently assert that dearth of interest is not an issue.
    I was some of the mud that got to sit up and look around.
    Lucky me. Lucky mud.
    -Kurt Vonnegut Jr.-
    Cat's Cradle.
    Reply With Quote  
     

  6. #5 Re: Strong foundation's! 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by GiantEvil
    Quote Originally Posted by DrRocket
    Quote Originally Posted by GiantEvil
    Is there a mental exercise which has a tendency to order the mind such that the understanding and retention of mathematical concepts, symbology, and algorithmic procedure is increased?
    Sometimes it seems to help if one is sober.
    While I intentionally enjoy the occasional buzz, I am by no means a drunkard. The only substance's I have ever meet the criteria for psychological and physiological addiction to is nicotine and caffeine, and I have wholly surrendered the use of nicotine, though I suspect that addiction itself will be with me to the end of my days. I am currently drinking a cup of coffee right now.

    Now, back to my original query.
    Say one want's to learn to juggle. It is good to start with one object, preferably uniform, and not to hard or bouncy. Then one assumes a rigid posture and practices throwing the object from one hand into the other with as minimal a movement as possible. This is the basic drill for developing the fundamental skill necessary to juggling.

    I am asking for a drill that strengthens the fundamental skill's necessary to the study and understanding of pattern and order.
    As an example, while travelling, picking two points on the horizon and using them, and myself as a third point, to visualize a triangle which would close down to a line segment as my ray of travel intersects the line segment formed by the two original points?

    Or, whenever a discernable group of object's fall's within my vision, I could consider them a set, count them to discover the cardinality of the set, then group the set into subsets based on arbitrary equivalence classes?

    Perhaps to never do a one to one count of objects in a geometric arrangement, but to always deduce their number from edge count and formula?
    Quote Originally Posted by MagiMaster
    You might want to look up recreational mathematics. It's not an exercise, but it might increase interest, which is probably more important.
    Thank you MagiMaster for the suggestion, though I can confidently assert that dearth of interest is not an issue.
    If you want exercises, get a copy of Topology: An Outline for a First Course by Lewis E. Ward and prove the theorems and work out the examples. It is relatively inexpensive on the used book market -- Amazon.com or Alibris.com

    This book is specifically designed for the reader to do his own proofs.

    It may help to brew a new pot of coffee.
    Reply With Quote  
     

  7. #6  
    Your Mama! GiantEvil's Avatar
    Join Date
    Apr 2010
    Location
    Vancouver, Wa
    Posts
    2,309
    Quote Originally Posted by DrRocket
    If you want exercises, get a copy of Topology: An Outline for a First Course by Lewis E. Ward and prove the theorems and work out the examples. It is relatively inexpensive on the used book market -- Amazon.com or Alibris.com

    This book is specifically designed for the reader to do his own proofs.
    I have ordered the book. It was affordable. Thanks.
    While were on books, I obtained a copy of Halmos's Naive Set Theory and found the exposition to be a little "fuzzy".
    I have found this alternative; http://www.amazon.com/Theory-Continu...9743025&sr=1-2
    I find it to be more rigorous, in depth, and clearer.

    And after all the calculus texts I've failed to get anything from, I find that I am getting somewhere with Morris Kline's Calculus book. Although his Wiki page gives me the impression that most mathematicians might consider him a pariah.
    I was some of the mud that got to sit up and look around.
    Lucky me. Lucky mud.
    -Kurt Vonnegut Jr.-
    Cat's Cradle.
    Reply With Quote  
     

  8. #7  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by GiantEvil
    Quote Originally Posted by DrRocket
    If you want exercises, get a copy of Topology: An Outline for a First Course by Lewis E. Ward and prove the theorems and work out the examples. It is relatively inexpensive on the used book market -- Amazon.com or Alibris.com

    This book is specifically designed for the reader to do his own proofs.
    I have ordered the book. It was affordable. Thanks.
    While were on books, I obtained a copy of Halmos's Naive Set Theory and found the exposition to be a little "fuzzy".
    I have found this alternative; http://www.amazon.com/Theory-Continu...9743025&sr=1-2
    I find it to be more rigorous, in depth, and clearer.

    And after all the calculus texts I've failed to get anything from, I find that I am getting somewhere with Morris Kline's Calculus book. Although his Wiki page gives me the impression that most mathematicians might consider him a pariah.
    I am a bit surprised at your feelings with regard to the book of Halmos. He is generally a model of clarity. I quite like that book. That said, it is naive set theory, not axiometric set theory. However, most mathematicians think in terms of naive set theory, and leave axiomeric set theory to logicians. There are exceptions, of course, and when real issues in set theory arise, there is no substitute for the axiometric approach. I do not know the book of Smulyian, yet. He is a logician. But I did order his book from Amazon, as well as Paul Cohen's book on the continuum hypothesis. Cohen is far more than a logician, and while he proved the independence of the continuum hypothesid, he also dif seminal work in harmonic analysis.

    Don't give up on Halmos. That is still a very good book and an excellent exposition of cardinal and ordinal numbers. In mathematics, I would describe it as "light reading".

    The only "good" calculus book of which I am aware is the (seldom used) book by Mike Spivak.

    BTW do not expevct to read Ward's book quickly. The proper waybto go through it is one theorem at a time, and proving each theorem before you go to the next one. You can expect to take a year, working hard and steadily, to get tjhrough the book.
    Reply With Quote  
     

  9. #8  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,620
    Quote Originally Posted by DrRocket
    Don't give up on Halmos {Naive Set Theory}. That is still a very good book and an excellent exposition of cardinal and ordinal numbers.
    I second these comments on the Halmos book, I enjoyed in immensely.

    It is often said that most mathematicians, real or aspiring, learn set theory by osmosis, a silly thing to say in my opinion, as it underpins all modern mathematics (though category theory is grooming itself for that role - fat chance!). Read and enjoy, it is not hard going.

    Forget axiomatic set theory, it is a very dry subject.

    The only "good" calculus book of which I am aware is the (seldom used) book by Mike Spivak.
    Yeah, why is it "seldom used"? What little calculus I ever had stomach for was taught me from James Stewart's book of the same name, which is thorough, but somewhat mechanical.

    I have Spivak, and, unlike Stewart, he explains the theory very well. I like it (but not enough to make me enjoy calculus).

    I also recommend Birkhoff & Mac Lane A Survey of Modern Algebra, which starts from the very "bottom" and covers just about everything except topology and differential geometry. Every statement is proved, plus there are loads of exercises (always a Good Thing)

    I got my copy from Alibris for about 10 euros.

    BTW, it was Saunders Mac Lane who founded category theory, and one can almost sense the idea of this starting to come to him as he writes this book. As I like category theory, maybe I am biased, but I recommend the book thoroughly.
    Reply With Quote  
     

  10. #9  
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Guitarist
    Quote Originally Posted by DrRocket
    Don't give up on Halmos {Naive Set Theory}. That is still a very good book and an excellent exposition of cardinal and ordinal numbers.
    I second these comments on the Halmos book, I enjoyed in immensely.

    It is often said that most mathematicians, real or aspiring, learn set theory by osmosis, a silly thing to say in my opinion, as it underpins all modern mathematics (though category theory is grooming itself for that role - fat chance!). Read and enjoy, it is not hard going.
    Silly or not, it is true.

    One can read and understand the Halmos book ober w weekend. Other than (yawn) axiomatic set theory, I have never seen a set theory class offered, and I have no idea what would be left to talk about after the first week if one were offered.

    The necessary topics are more than adequately covered in the introductions to real analysis, topology and algebra, including one's preferred version of the axiom of choice -- the axiom itself, Zorn's lemmsa, Hausdorff maximum principle.

    Category theory is useful language, but is not likely to ever be regarded as "underpinning everything".

    Quote Originally Posted by guitarist
    I also recommend Birkhoff & Mac Lane A Survey of Modern Algebra, which starts from the very "bottom" and covers just about everything except topology and differential geometry. Every statement is proved, plus there are loads of exercises (always a Good Thing)

    I got my copy from Alibris for about 10 euros.

    BTW, it was Saunders Mac Lane who founded category theory, and one can almost sense the idea of this starting to come to him as he writes this book. As I like category theory, maybe I am biased, but I recommend the book thoroughly.
    Birkhoff & MacLane is a fine algebra book, if a bit dated, for an introduction to algebra and number systems. It is not a substitute for books on analysis or topology. It does tend to dwell on the obvious at times.
    Reply With Quote  
     

  11. #10  
    Your Mama! GiantEvil's Avatar
    Join Date
    Apr 2010
    Location
    Vancouver, Wa
    Posts
    2,309
    I don't know if you're lurking around Doc, but I got that topology book the other day. I've given it a cursory examination but haven't dived in yet. I was expecting some pictures of donuts, but don't see any. Oh well.
    I'm currently rather indulged in "A Book of Abstract Algebra" by Charles C. Pinter.
    Anyhow, I was wondering if you had received your "Set Theory" by Smullyan yet. What do you think?
    Set theory isn't hard, but it is a little tedious. The first order logic symbology in the Smullyan book threw me off a little, but there's a lot of context available, and The Wiki to reference, so I think I got a good handle on it now.
    I was some of the mud that got to sit up and look around.
    Lucky me. Lucky mud.
    -Kurt Vonnegut Jr.-
    Cat's Cradle.
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •