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  1. MidgetDwarf

    What impact has the COVID-19 pandemic had on your job?

    I am only working 5 hours a week at 20 dollar an hour before taxes. Needeless to say, I an doing badly. I needed $130 to pay my monthly credit card statement. However, I used the $130 to purchase 3 books: Munkres Topology (2nd Ed/Hardcover), Simmons Topology and Modern Analysis, and Visual...
  2. MidgetDwarf

    I Reference For The Historical Context of Dedekind Cuts and Why the need

    I was wondering if anyone knew of sources regarding the history of Dedekind Cuts and its use to construct the Reals. Ie., the mathematical thinking leading to this idea, why it is important, and how it allowed to put Analysis on a rigorous foundation.
  3. MidgetDwarf

    Medical What is benign etymology?

    What really piqued my interest was reading: The Autobiography of Malcom X. In particular, how he breaks down the word of demagogue, its original meaning and how it changed.
  4. MidgetDwarf

    Programs Is this an indication that I should stay away from higher math?

    How do you like it so far? The first section can be a bit weird for most newcomers. So maybe you do not like this section, but it gets way better. Have you arrived to the discussion of a parabola, a neat discussion of snells law, and parabolic sector? What I found very cool was the discussion of...
  5. MidgetDwarf

    I Help Finding the Correct Approach to this Proof (Intro Real Analysis)

    Thank you. Ill have a more thorough look at it in the upcoming months. At the time, the book went over my head, but I was able to learn a few things from it. Never cared to much about foundational stuff, but my interest has grown seeing some interesting problems on mathstacks.
  6. MidgetDwarf

    Medical What is benign etymology?

    Not related to biology. But my knowledge of etymology increased by reading (novels, autobiography, simple things). When. I started noticing combination of letters attached to words frequently. So I investigated.
  7. MidgetDwarf

    Courses Deciding What Math Courses to Take Next

    You should inquire about how the Complex Analysis Course is taught at your university. It can be a very applied course, a theoretical math course, or a mixture of both. Moreover, to make sense of it, it is easier to know some Analysis on R, which would be an intro Analysis course. Have you taken...
  8. MidgetDwarf

    Analysis Lectures That Follow Pugh: Real Mathematical Analysis

    Not sure if this is the correct forum. But are there any video lectures that follow the book Pugh: Real Mathematical Analysis? Thanks.
  9. MidgetDwarf

    I Help Finding the Correct Approach to this Proof (Intro Real Analysis)

    @ Mathwonk. I think the definition a set is finite iff it has only a finite set of distinct objects, comes from Halmos:Naive Set Theory. IRC it ignores Russels Paradox, so it gives that definition. I can be wrong. I read it many years ago when I was still in a remedial trigonometry class. So I...
  10. MidgetDwarf

    I Self teaching analysis and topology

    Analysis was one of those math courses that was difficult to learn from books, compared to say Modern Algebra books. To my eyes, it seems that Analysis is more difficult to learn. Since I want to be an Analyst or a Geometer, I need to practice more Analysis. End of my rant. The book that I...
  11. MidgetDwarf

    Programs Is this an indication that I should stay away from higher math?

    Out of print. But if you are able to read a non-English language, then its a lot cheaper. Ie., Spanish, can be had for $50 for all 3. Russian for $40., etc..
  12. MidgetDwarf

    Programs Is this an indication that I should stay away from higher math?

    If you are still interested in a calculus based physics. Look into Alonso And Finn: University Physics. It is a neat book that does not shy away from the calculus. Almost everything has a derivation. The series is pricey, maybe around $300 to $500, but since you are a Doctor, it won't hurt your...
  13. MidgetDwarf

    Foundations Rigorous Alternatives to AoPS for PreAlgebra-PreCalculus?

    For Trigonometry: Look up the author S L Looney. It can be hard to read at points, but I learned a lot from it. Granted, when I read the book I was taking Calculus 3. I’m sure it’s an easy read now for me. I good reminder is that what one sees as difficult may not be so in the future. So I...
  14. MidgetDwarf

    Other Did I choose the right books for relearning math (Geometry, Algebra, Logic and Proofs)?

    Yes. Teaching is an art. I have a very intelligent teacher (numerous publications). However, his lecture just goes over my head. He does try to explain it so that students understand. But sometimes, while taking a bath or walking. Things click. I can replay some of his lectures by memory years...
  15. MidgetDwarf

    I Is this a Linear subspace?

    Yes. I also speak Spanish and this is true.
  16. MidgetDwarf

    What Have Educators Learned About Distance Learning?

    Is there any difference or difficulties that arises with the teaching of pure mathematics during this event? I think this is the least affected area.
  17. MidgetDwarf

    Other Did I choose the right books for relearning math (Geometry, Algebra, Logic and Proofs)?

    I would hold off on buying any more sources. You have enough to last at least 2 years. The Gelfand book on trig is very neat, although it lacks problems/topics. But everything contained within it is lucid. There is a neat proof of the Pythagorean theorem, that is not so trivial. It uses some...
  18. MidgetDwarf

    Other Did I choose the right books for relearning math (Geometry, Algebra, Logic and Proofs)?

    Glad you liked Moise. I find his exposition very clear, informative, and sometimes funny. However, his Elementary Geometry From An Advance Standpoint, can be sometimes dry. Its a good book tho, but many people confuse the audience which the book is aimed for, ie., the elementary part. This kind...
  19. MidgetDwarf

    Other Did I choose the right books for relearning math (Geometry, Algebra, Logic and Proofs)?

    I personally don’t care for the art of problem solving books. But I’m into pure mathematics. You can just skip Spivak, and go straight to Analysis (Abbot) but im not sure how that would fit into your career goals. For an applied math book. Moise Calculus or Thomas Calculus 3rd edition...
  20. MidgetDwarf

    Other Did I choose the right books for relearning math (Geometry, Algebra, Logic and Proofs)?

    Great. Hopefully nothing changed to much from the first to that one. Typically, older editions of books are better. Take for instance Thomas Calculus With Analytic Geometry 3rd to the editions after (5th I think). It Is not the same book. The 3rd edition of Thomas is a gem, although an applied...
  21. MidgetDwarf

    Other Did I choose the right books for relearning math (Geometry, Algebra, Logic and Proofs)?

    https://www.thriftbooks.com/w/geometry_floyd-l-downs-jr/257493/item/5956128/#isbn=0201050285&idiq=5956128 here is a cheap edition. im not sure which edition it is. but you won't loose to much. if you add $3.20 with an extra book, you get free shipping. I think its the second. I have only seen...
  22. MidgetDwarf

    Other Did I choose the right books for relearning math (Geometry, Algebra, Logic and Proofs)?

    Also, purchase a nice compass. You can be a bit cheap with the straightedge (fold an edge of paper in half), but not so much the compass.
  23. MidgetDwarf

    Other Did I choose the right books for relearning math (Geometry, Algebra, Logic and Proofs)?

    Yes, its a very common error between his two geometry books. However, the one people recommended is the Moise/Downs. I own the first edition. Hmm. I would not recommend right after Kisselev, but it is doable. Theres some Analysis and Algebra (Modern) hidden within the book. It is also devoid of...
  24. MidgetDwarf

    Other Did I choose the right books for relearning math (Geometry, Algebra, Logic and Proofs)?

    The Lang book is good. But the geometry book from Moise is not appropriate for you at this point. It’s an advanced book on geometry. I have a bachelors in mathematics and I remember going through it my last semester In undergrad. Instead, for geometry. I would recommend Moise/Downs Geometry...
  25. MidgetDwarf

    Solving an exact differential equation

    I think reading the relevant definitions and the notation used , the integrand and its "neighbors", would clarify some of the issues you have. I think its more notational on your part then anything. Any modern calculus book has this.
  26. MidgetDwarf

    Calculus Textbook for differentials

    An older book, would be the one by Ross. Im to lazy to look at the table of contents of your book, But Ross: Differential Equations, is a very good introduction to the subject that also has enough content for a second course. The best book on differential equations is by Arnold, but that's an...
  27. MidgetDwarf

    Classical Introductory rigorous books on Electromagnetism

    hmm. Read the section on kinematics in Alonso, then compare it to HRW and Serway. Alonso actually derives the general form (3-dimension as seen in Calculus 3. But HRW and Serway do not. Moreover, the diagrams in Alonso are memorable.
  28. MidgetDwarf

    Classical Introductory rigorous books on Electromagnetism

    Yes. Alonso does not skimp on mathematics. neat derivations, which allows readers to think how the theory is connected. Beautiful explanation of the Lorentz transformation, momentum. etc. Problems are way easier than Purcell, but they compliment each other so well. The beauty of Alonso comes in...
  29. MidgetDwarf

    Courses Complex Analysis Courses or Complex Variable Courses?

    Can you take the theory class, and then just apply the application of the theory to physics problems? The Churchill Book is nice, has some proofs in it. But I would supplement it with a book that shows a more geometric approach to Complex Analysis.
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