A Course in Calculus and Real Analysis (Undergraduate Texts in Mathematics)
Contents:
The Pleasures of Probability, An Accompaniment to Higher Mathematics, Variational Calculus and Optimal Control: Optimization with Elementary Convexity, 2. Gerard Buskes, Arnoud Van Rooij: From Distance to Neighborhood, Benjamin Fine, Gerhard Rosenberger: The Fundamental Theorem of Algebra, A New Approach to Real Analysis,. Introduction to Coding and Information Theory, Rings, Fields, and Vector Spaces: In a Room with Many Mirrors, Basic Elements of Real Analysis, A Liberal Art, 2. Plane and Fancy, Applied Abstract Algebra, 2. Numbers and Geometry, Reinhard Laubenbacher, David Pengelley: Chronicles by the Explorers, Theory and Applications, Bruce van Brunt, Michael Carter: A Practical Introduction, Euclid and Beyond, The Geometry of Spacetime: An Introduction to Special and General Relativity, A Course in Modern Geometries, 2.
The Art of Enumerative Combinatorics, From a Room with Many Windows, Beginning Functional Analysis, Practical Analysis in One Variable, Glimpses of Algebra and Geometry, 2. Farid Aitsahlia, Kai Lai Chung: Topics in the Theory of Numbers, Elementary and Beyond, Elements of Number Theory, Johannes Buchmann ; Introduction to Cryptography, 2.
Integers, Polynomials, and Rings: A Course in Algebra, An Introduction with Mathematica, 2. From Rabbits to Chaos, A Field Guide to Algebra, An Introduction to Difference Equations, 3.
Linearity, Symmetry, and Prediction in the Hydrogen Atom, The Four Pillars of Geometry, A Course in Calculus and Real Analysis, A Concrete Introduction to Algebraic Curves, 2. Notes on Set Theory, 2. Further Chronicles by the Explorers, Applied Linear Algebra and Matrix Analysis, Combinatorics and Graph Theory, 2. Naive Lie Theory, Ernst Hairer , Gerhard Wanner: Analysis by its History, zuerst Measure, Topology, and Fractal Geometry, 2. James Herod, Ronald W. An Introduction with Maple and Matlab, 2.
A Course in Calculus and Real Analysis
Frank Mendivil, Ronald W. Explorations in Monte Carlo Methods, Primes, Congruences, and Secrets: A Computational Approach, Home Questions Tags Users Unanswered. Text for an introductory Real Analysis course. I don't know if this is the right place to be asking this question. In any case, please explain what " level" means.
I'm guessing that this is US terminology; those outside your country won't necessarily know what it means. Voting -1 for lack of clarity. I'm in the US, and I don't know what level means. I think this is university-specific. I have known universities where means lower-division undergrad, upper-division undergrad, and graduate, and where there are no courses with such numbering. At the liberal arts school that I've attended introductory real analysis is in the s. Questions like this i. I've hit it with the wiki-hammer. I recommended this book yesterday it even got 2 votes but my answer seems to have vanished Your answer didn't vanish.
I edited it to add links, and answer the second part of the question. After reading some of this book I have to say I really like it. Many of my complaints about some of the other books that I was looking at were not clear in my head until I saw the same topic in Abbott's book and saw how he explains the purpose of the theorems he presents rather than just giving the theorem and proof. I think for an introductory class students will benefit from that exposition. Just to clarify, does this book assume students entering the course already have a basic calculus background?
The review seems to indicate that.
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Not much sense avoiding calculus as a prerequisite. For average students,who have never seen proofs before, I strongly recommend Ross' Elementary Analysis: The Theory Of Calculus. It's gentle, complete and walks the reader through a careful presentation of calculus containing many steps that are usually omitted or left as an exercise. It can also be used for an honors calculus course: I've had friends that have used it for that purpose with great success.
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Spivak is a beautiful book at roughly the same level that'll work just as well. It's an amazingly deep and complete text on normed linear spaces rather then metric or topological spaces and focuses on WHY things work in analysis as they do. Lastly, for honor students on their way to elite PHD programs, we now have a wonderful alternative to Rudin and I'm shocked no one's mentioned it at this thread yet: Charles Chapman Pugh's Real Mathematical Analysis , which developed out of the author's honors analysis courses at Berkeley.
It's terse but written with crystal clarity and with hundreds of well-chosen pictures and hard exercises. Pugh has a real gift that's on display here. I've never seen any author who does this as effectively as Pugh. The many, many pictures greatly assist him in this task: Even if it's just to make a joke see the cornball pic in chapter one showing a Dedekind cut,ugh.
Rudin covers some important points of point-set topology that are simply not covered in any other introductory analysis book. Students in an "honors calculus" course at the level of math 55 at Harvard real analysis in disguise who do not see a fairly significant portion of point-set topology by the end of the first semester are in my opinion being done a huge disservice.
Undergraduate Texts in Mathematics A Course in Calculus and Real Analysis inadequately covered in calculus courses and glossed over in real analysis. Undergraduate Texts in Mathematics A Course in Calculus and Real Analysis a unified exposition of single‐variable calculus and classical real analysis.
Your first sentence on Rudin's book is very bad, unfair and very likely not true. Any serious college student who approaches analysis for the first time must know what a proof is, having seen it in Euclidean Geometry back in junior middle school. And I personally like Rudin's, read it when I was still in high school and found it clear, to-the-point, and with a good supply of excellent problems.
Also, one cannot fault an author for giving slick proofs. I for one prefer slick proofs over tedious, drawn-out proofs unless they're the correct conceptual ones. A great deal of point set theory is covered in Pugh and done more clearly then in Rudin. I don't know where Anonymous was trained,but clearly came from a better system then most students come from.
Most high schools in America in have trouble graduating students who can READ,let alone know geometry.
I have known universities where means lower-division undergrad, upper-division undergrad, and graduate, and where there are no courses with such numbering. Naive Lie Theory John Stillwell. The Mathematics of Nonlinear Programming, Ghorpade , Balmohan V. Heinz-Dieter Ebbinghaus , J. A google preview can be found at https: Buskes, Gerard; Rooij, Arnoud Van
It's easy to like slick proofs when you're experienced and well-versed in rigor. Most instructors don't remember what it was like struggling with that fundamental change in thinking that proof creates the first time. Worse,gifted students think anyone that doesn't find it easy is an imbecile. The collapse of the American secondary school system has sadly affected incoming 1st year math students more then any group. We need to adjust the analysis texts accordingly. The students are NOT "dumber" then in previous generations-as a lot of better trained students snark nowadays-they're simply very poorly prepared.
Daniel Take a good,careful look at Pugh's book,especially the exercises. I think you'll find it far superior to Rudin while still remaining terse and concise. I haven't read any of the books suggested by AndrewL so I'm not going to comment on whether they are any good. Rudin is too difficult for a first course simply because they have not been prepared well enough just look up any recent high school text.
It would certainly make a great text for a follow-up course after one has acquired the fundamentals of analysis though. Rudin's Principles of Mathematical Analysis. I also dip into a few others on a regular basis: Product details Format Hardback pages Dimensions x x Illustrations note X, p. Looking for beautiful books?
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Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. Other books in this series. Understanding Analysis Stephen Abbott. Mathematics and Its History John Stillwell. Naive Lie Theory John Stillwell.
Undergraduate Texts in Mathematics
Complex Analysis Joseph Bak. Introduction to Cryptography Johannes Buchmann. Elementary Analysis Kenneth Allen Ross. Combinatorics and Graph Theory John M.
Groups and Symmetry Mark A. Discrete Mathematics Laszlo Lovasz. Euclid and Beyond Robin Hartshorne. Linear Algebra Serge Lang. Back cover copy This book provides a self-contained and rigorous introduction to calculus of functions of one variable.