What you need to do is disciplined review and practice of the basics. Any standard review (or even omnibus) text will be "correct enough" for you to get value. You need to work on the basics.need to acquire automaticity in manipulations involving trig, power laws, logs, etc. Given, the totality of what you said (taken only through Calc 1, need to review pre-calc), you're not the candidate for stuff that is more difficult. Or at least not the way many people on MSE or MESE use it (highly abstract, very difficult). That is probably not what you really need. I would just be careful about using the word "rigor". I am trying to address the real question, I think you are asking. Even if it's not perfect, at least you are familiar with it. Other than that, if you have access to your old calculus 1 text, I recommend looking at it. These intellectuals transformed the uses of calculus from problem-solving. This text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his peers. One of the reasons you are having to review is likely lack of drill earlier.) The Origins of Cauchy's Rigorous Calculus. And you can decide how much to read versus practice. Has example problems and exercises, with answers. (You'll need something else, preferably not a doorstop but something of a review nature or "for business students" or the like.) Im not sure if they cover all of the precalculus curriculum, though. Ive been looking at the books by Gelfand (Algebra, Trigonometry, Functions and Graphs, The Method of Coordinates). Not a ganglion-basher.Ĭovers first and second year HS algebra, plane and solid geometry, plane trig, analytical geometry, function concept, and very short/easy intro to calculus (pre-calc style). can prepare you for rigorous calculus texts like Spivak and Apostol. Directed at the student as the customer, not a committee of teachers. Since it is a review, it is written economically and clearly. I have/like the original 1958 edition (easy to get used), but the newer edition with co-author is probably OK, also. It was published in 1891, about the time of my grand-grand father! It contains a plethora of information!įrank Ayres First Year College Math (Schaum's Outline). SECOND EDIT: I've found the book I was looking for, after browsing a bunch of similar threads, I've found the precious jewel: A rigorous text would be: 'Multivariable Calculus' by Ted Shifrin (who spent years, working get the course right) however Rogawski + Lang were rigorous enough for me to teach from. I meant a book that is challenging, a bit formal in nature, and includes useful and fruitful topics not usually found in traditional maths textbooks. Where should I begin? What book(s) should I go with? Is there a list?ĮDIT: Clarification on my use of the word "rigor": My geometry & trig has also gotten a bit rusty over the months. They oversimplify everything and bloat the book with unnecessary figures explaining basic things, and their countless excercises also provide no real value as all they require is rote memorization of the given techniques. I am aware it's too much to ask for a single book and that supplementary material is available through other books, but my problem is that these modern books aren't rigorous enough in their text. I was hoping for a book that would include comprehensive & rigorous text on precalculus, probability & combinatorics, and analysis. But it's been a couple months since I've done any solid mathematics. The story, of course, does not end with Cauchy, but this excellent and enticing book actually centers its action on the work previous to Cauchy's as well as on Cauchy's own achievements: in it, the importance of Euler, D'Alembert, Ampère, Poisson, Lagrange (of course), and the unjustly somewhat forgotten Bernand Bolzano, is properly addressed, in addition to a very stimulating account of Cauchy's own work.I've taken Calculus 1 and it's time to relearn because I've forgotten some of it. He was one, admitedly a very important one, of a plethora of great mathematicians that helped build one of the most impressive of humanity's intellectual achievements: the rigorous foundations of Mathematical Analysis. His importance in shaping the field and definitely steering the subject into the rigorous mathematical discipline we know today, can be gauged by the number of times his name appears connected with mathematical objects and results of present day currency (Cauchy sequence, Cauchy criterion for series, Cauchy root test, Cauchy-Hadamard theorem, the Cauchy-Riemann equations, the Cauchy integral formulas.) this not to speak of the very notion of limit and continuity, whose rigorous definition is very much Cauchy's work, or the first rigorous definition of integral (now disused, but nevertheless of historical interest.) However great Cauchy was, he did not work alone or ab initio. Augustin-Louis Cauchy was one of the giants of nineteen century's Mathematical Analysis.
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