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 Tao, Terence, 1975
 Oxford ; New York : Oxford University Press, 2006.
 Description
 Book — xii, 103 p. : ill. ; 24 cm.
 Summary

 Preface
 1. Strategies in problem solving
 2. Examples in number theory
 3. Examples in algebra and analysis
 4. Euclidean geometry
 5. Analytic geometry
 6. Sundry examples References Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level. Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.
(source: Nielsen Book Data)
 Online
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QA300 .T326 2006  Unknown 
2. Complex analysis [2003]
 Howie, John M. (John Mackintosh)
 London ; New York : Springer, 2003.
 Description
 Book — xi, 260 p. : ill. ; 24 cm.
 Summary

 What Do I Need to Know? Complex Numbers. Prelude to Complex Analysis. Differentiation. Complex Integration. Cauchy's Theorem. Some Consequences of Cauchy's Theorem. Laurent Series and the Residue Theorem. Applications of Contour Integration. Further Topics. Conformal Mappings. Final Remarks. Solutions to Exercises. Bibliography. Index.
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QA300 .H692 2003  Unknown 
 Saff, E. B., 1944
 3rd ed.  Upper Saddle River, N.J. : Prentice Hall, c2003.
 Description
 Book — xi, 511 p. : ill. ; 23 cm.
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

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QA300 .S18 2003  Unknown 
4. Analysis on fractals [2001]
 Kigami, Jun.
 Cambridge ; New York : Cambridge University Press, 2001.
 Description
 Book — viii, 226 pages : illustrations ; 24 cm.
 Summary

 Geometry of selfsimilar sets
 Analysis on limits of networks
 Construction of laplacians on P.C.F. self similar structures
 Eigenvalues and eigenfunctions of laplacians
 Heat kernels.
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Science Library (Li and Ma)
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QA614.86 .K54 2001  Unknown 
5. Complex analysis [2001]
 Gamelin, Theodore W.
 New York : Springer, c2001.
 Description
 Book — xviii, 478 p. ; 24 cm.
 Summary

 The Complex Plane and Elementary Functions. Analytic Functions. Line Integrals and Harmonic Functions. Complex Integration and Analyticity. Power Series. Laurent Series and Isolated Singularities. The Residue Calculus. The Logarithmic Integral. The Schwarz Lemma and Hyperbolic Geometry. Harmonic Functions and the Reflection Principle. Conformal Mapping. Compact Families of Meromorphic Functions. Approximation Theorems. Some Special Functions. The Dirichlet Problem. Riemann Surfaces.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. The book consists of three parts. The first part comprises the basic core of a course in complex analysis for junior and senior undergraduates. The second part includes various more specialized topics such as the argument principle, the Schwarz lemma and hyperbolic geometry, the Poisson integral, and the Riemann mapping theorem. The third part consists of a selection of topics designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics selected include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries, spherical, euclidean, and hyperbolic, are stressed. Exercises range from the very simple to the quite challenging, in all chapters. The book is based on lectures given over the years by the author at several places, particularly the Interuniversity Summer School at Perugia (Italy), and also UCLA, Brown University, Valencia (Spain), and La Plata (Argentina). A native of Minnesota, the author did his undergraduate work at Yale University and his graduate work at UC Berkeley. After spending some time at MIT and at the Universidad Nacional de La Plata (Argentina), he joined the faculty at UCLA in 1968.
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Science Library (Li and Ma)
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QA300 .G25 2001  Unknown 
6. Understanding analysis [2001]
 Abbott, Stephen, 1964
 New York : Springer, c2001.
 Description
 Book — xii, 257 p. : ill. ; 24 cm.
 Summary

 1 The Real Numbers. 1.1 Discussion: The Irrationality of % MathType!MTEF!2!1!+ % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqJc9 % vqaqpepm0xbba9pwe9Q8fs0yqaqpepae9pg0FirpepeKkFr0xfrx % frxb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaaSbdaGcaa % qaaiaaikdaaSqabaaaaa!3794! $$\sqrt
 2 $$. 1.2 Some Preliminaries. 1.3 The Axiom of Completeness. 1.4 Consequences of Completeness. 1.5 Cantor's Theorem. 1.6 Epilogue.
 2 Sequences and Series. 2.1 Discussion: Rearrangements of Infinite Series. 2.2 The Limit of a Sequence. 2.3 The Algebraic and Order Limit Theorems. 2.4 The Monotone Convergence Theorem and a First Look at Infinite Series. 2.5 Subsequences and the BolzanoWeierstrass Theorem. 2.6 The Cauchy Criterion. 2.7 Properties of Infinite Series. 2.8 Double Summations and Products of Infinite Series. 2.9 Epilogue.
 3 Basic Topology of R. 3.1 Discussion: The Cantor Set. 3.2 Open and Closed Sets. 3.3 Compact Sets. 3.4 Perfect Sets and Connected Sets. 3.5 Baire's Theorem. 3.6 Epilogue.
 4 Functional Limits and Continuity. 4.1 Discussion: Examples of Dirichlet and Thomae. 4.2 Functional Limits. 4.3 Combinations of Continuous Functions. 4.4 Continuous Functions on Compact Sets. 4.5 The Intermediate Value Theorem. 4.6 Sets of Discontinuity. 4.7 Epilogue.
 5 The Derivative. 5.1 Discussion: Are Derivatives Continuous?. 5.2 Derivatives and the Intermediate Value Property. 5.3 The Mean Value Theorem. 5.4 A Continuous NowhereDifferentiable Function. 5.5 Epilogue.
 6 Sequences and Series of Functions. 6.1 Discussion: Branching Processes. 6.2 Uniform Convergence of a Sequence of Functions. 6.3 Uniform Convergence and Differentiation. 6.4 Series of Functions. 6.5 Power Series. 6.6 Taylor Series. 6.7 Epilogue.
 7 The Riemann Integral. 7.1 Discussion: How Should Integration be Defined?. 7.2 The Definition of the Riemann Integral. 7.3 Integrating Functions with Discontinuities. 7.4 Properties of the Integral. 7.5 The Fundamental Theorem of Calculus. 7.6 Lebesgue's Criterion for Riemann Integrability. 7.7 Epilogue.
 8 Additional Topics. 8.1 The Generalized Riemann Integral. 8.2 Metric Spaces and the Baire Category Theorem. 8.3 Fourier Series. 8.4 A Construction of R From Q.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA300 .A18 2001  Unknown 
7. The way of analysis [2000]
 Strichartz, Robert S.
 Rev. ed.  Boston : Jones and Bartlett Publishers, c2000.
 Description
 Book — xix, 739 p. : ill. ; 24 cm.
 Online
Science Library (Li and Ma)
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QA300 .S888 2000  Unavailable Ask at circulation desk 
8. A first course in real analysis [1991]
 Protter, Murray H.
 2nd ed.  New York : SpringerVerlag, c1991.
 Description
 Book — xviii, 534 p. : ill. ; 24 cm.
 Summary

 The Real Number System. Continuity and Limits. Basic Properties of Functions on R. Elementary Theory of Differentiation. Elementary Theory of Integration. Elementary Theory of Metric Spaces. Differentiation in R. Integration in R. Infinite Sequences and Infinite Series. Fourier Series. Functions Defined by Integrals.Improper Integrals. The RiemannStieltjes Integral and Functions of Bounded Variation. Contraction Mappings, Newton's Method, and Differential Equations. Implicit Function Theorems and Lagrange Multipliers. Functions on Metric Spaces. Approximation. Vector Field Theory the Theorems of Green and Stokes. Appendices.
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 Online
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QA300 .P968 1991  Unknown 
9. Methods of real analysis [1976]
 Goldberg, Richard R.
 2d ed.  New York : Wiley, ©1976.
 Description
 Book — x, 402 pages : illustrations ; 27 cm
 Summary

 Partial table of contents: Sets and Functions. Sequences of Real Numbers. Series of Real Numbers. Limits and Metric Spaces. Continuous Functions on Metric Spaces. Connectedness, Completeness, and Compactness. Calculus. The Elementary Functions. Taylor Series.
 (source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

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QA331.5 .G58 1976  Unknown 
10. Analysis in Euclidean space [1975]
 Hoffman, Kenneth.
 Englewood Cliffs, N.J., PrenticeHall [1975]
 Description
 Book — xiv, 432 p. illus. 24 cm.
 Online
SAL3 (offcampus storage), Science Library (Li and Ma)
SAL3 (offcampus storage)  Status 

Stacks  Request 
QA300 .H63  Available 
Science Library (Li and Ma)  Status 

Stacks  
QA300 .H63  Unknown 