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An Introduction to Higher Mathematics

An Introduction to Higher Mathematics
2 Volume Set


Part of The Cambridge China Library

  • Date Published: May 2012
  • availability: Available
  • format: Multiple copy pack
  • isbn: 9781107020016

$ 162.00
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About the Authors
  • The self-taught mathematician Hua Loo-Keng (1910–1985) has been credited with inspiring generations of mathematicians, while his papers on number theory are regarded as some of the most significant contributions made to the subject during the first half of the twentieth century. An Introduction to Higher Mathematics is based on the lectures given by Hua at the University of Science and Technology of China from 1958. The course reflects Hua's instinctive technique, using the simplest tools to tackle even the most difficult problems, and contains both pure and applied mathematics, emphasising the interdependent relationships between different branches of the discipline. With hundreds of diagrams, examples and exercises, this is a wide-ranging reference text for university mathematics and a testament to the teaching of one of the most eminent mathematicians of his generation.

    • The first English translation of Hua's lectures, featuring a newly commissioned introduction from Professor Heini Halberstam
    • Covers a broad range of subjects in both pure and applied mathematics that are still highly relevant to advanced undergraduate and postgraduate study
    • Demonstrates Hua's instinctive technique and his successful use of first principles and concrete examples to approach complex problems
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    Product details

    • Date Published: May 2012
    • format: Multiple copy pack
    • isbn: 9781107020016
    • length: 900 pages
    • dimensions: 253 x 178 x 75 mm
    • weight: 3.22kg
    • availability: Available
  • Table of Contents

    Volume I:
    1. Real and complex numbers
    2. Vector algebra
    3. Functions and graphs
    4. Limits
    5. The differential calculus
    6. Applications of the derivative
    7. Taylor expansions
    8. Approximate solutions to equations
    9. Indefinite integrals
    10. Definite integrals
    11. Applications of integral calculus
    12. Functions of several variables
    13. Sequences, series and integrals with variables
    14. Differential properties of curves
    15. Multiple integral
    16. Curvilinear integral and surface integral
    17. Scalar field and vector field
    18. Differential properties of curved surfaces
    19. Fourier series
    20. System of ordinary differential equations. Volume II:
    1. Geometry of the complex plane
    2. Non-Euclidean geometry
    3. Definitions and examples of analytic and harmonic functions
    4. Harmonic functions
    5. Some basic concepts in point set theory and topology
    6. Analytic functions
    7. Residues and their application to definite integral
    8. Maximum modulus principle and the family of functions
    9. Entire function and meromorphic function
    10. Conformal transformation
    11. Summation
    12. Harmonic functions under various boundary conditions
    13. Weierstrass' elliptic function theory
    14. Jacobi's elliptic functions
    15. Systems of linear equations and determinants (review outline)
    16. Equivalence of matrices
    17. Functions, sequences and series of square matrices
    18. Difference equations with constant coefficients and ordinary differential equations
    19. Asymptotic property of solutions
    20. Quadratic form
    21. Orthogonal groups and pair of quadratic forms
    22. Volumes
    23. Non-negative square matrices. Volume III:
    1. The geometry of the complex plane
    2. Non-Euclidean geometry
    3. Definitions and examples of analytic functions and harmonic functions
    4. Harmonic functions
    5. Point set theory and preparations for topology
    6. Analytic functions
    7. The residue and its application to evaluation of definite integrals
    8. Maximum modulus theorem and families of functions
    9. Integral functions and metamorphic functions
    10. Conformal transformations
    11. Summability methods
    12. Harmonic functions satisfying various types of boundary conditions
    13. Weierstrass elliptic function theory
    14. Jacobian elliptic function theory. Volume IV:
    1. Linear systems and determinants (review)
    2. Equivalence of matrices
    3. Functions, sequences and series of square matrices
    4. Difference and differential equations with constant coefficients
    5. Asymptotic properties of solutions
    6. Quadratic forms
    7. Orthogonal groups corresponding to quadratic forms
    8. Volumes
    9. Non-negative square matrices.

  • Author

    Loo-Keng Hua, Chinese Academy of Sciences
    Hua Loo-Keng (1910–1985), a self-taught mathematician, is remembered as one of the leading scholars of his time. Hua spent most of his working life in China and suffered at first hand the turbulence of twentieth-century Chinese politics – but he also travelled extensively. This included time spent at Cambridge in the 1930s, when he made notable contributions to number theory, and post-war visits to Russia and America. Hua was appointed a professor of mathematics at the University of Illinois in 1949, but he chose instead to return to China to train the next generation of mathematicians and became the first director of the Mathematical Institute of the Academia Sinica. He was later appointed vice-president of Academia Sinica and a science advisor to his government. He continued to study and lecture abroad until his death in Tokyo in 1985. Hua received honorary degrees from the University of Nancy (1980), the Chinese University of Hong Kong (1983) and the University of Illinois (1984). His work has been translated into many languages, and Hua was elected a foreign associate of the National Academy of Sciences in 1982 and a member of the Deutsche Akademie der Naturforscher Leopoldina (1983), the Academy of the Third World (1983) and the Bavarian Academy of Sciences (1985).


    Peter Shiu, Loughborough University
    Peter Shiu, now retired, was Reader in Pure Mathematics at Loughborough University. He has published widely on his own research interests and was the translator of Hua Loo-Keng's Introduction to Number Theory (1982) and Hua Loo-Keng by Wang Yuan (1998).

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