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This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of the methods that are used.

We have avoided that style which gives a systematic development of the apparatus and have used instead a freer style, in which the problems and the methods of solution are closely interwoven. We start from concrete problems in number theory. General theories arise as tools for solving these problems. As a rule, these theories are developed sufficiently far so that the reader can see for himself their strength and beauty, and so that he learns to apply them.

Most of the questions that are examined in this book are connected with the theory of diophantine equations - that is, with the theory of the solutions in integers of equations in several variables. However, we also consider questions of other types; for example, we derive the theorem of Dirichlet on prime numbers in arithmetic progressions and investigate the growth of the number of solutions of congruences.

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Topological Vector Spaces, Distributions and Kernels

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Topological Vector Spaces, Distributions and Kernels

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Resolution of Singularities of Embedded Algebraic Surfaces

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Resolution of Singularities of Embedded Algebraic Surfaces

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Partial Differential Equations in Physics

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The topic with which I regularly conclude my six-term series of lectures in Munich is the partial differential equations of physics. We do not really deal with mathematical physics, but with physical mathematics; not with the mathematical formulation of physical facts, but with the physical motivation of mathematical methods. The oftmentioned prestabilized harmony between what is mathematically interesting and what is physically important is met at each step and lends an esthetic - I should like to say metaphysical -- attraction to our subject.

The problems to be treated belong mainly to the classical matherhatical literature, as shown by their connection with the names of Laplace, Fourier, Green, Gauss, Riemann, and William Thomson. In order to show that these methods are adequate to deal with actual problems, we treat the propagation of radio waves in some detail in Chapter VI.

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The Alkaloids: Chemistry and Pharmacology

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The Alkaloids: Chemistry and Pharmacology

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The Alkaloids: Chemistry and Pharmacology

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The Alkaloids: Chemistry and Pharmacology

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The Alkaloids: Antitumor Bisindole Alkaloids from Catharanthus roseus (L.)

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The Alkaloids: Antitumor Bisindole Alkaloids from Catharanthus roseus (L.)

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The Alkaloids: Chemistry and Pharmacology

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The Alkaloids: Chemistry and Pharmacology

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The Alkaloids: Chemistry and Pharmacology

# data[].attributes.description
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.name
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.description
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.name
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.description
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.name
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.description
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.name
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.description
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.name
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.description
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.name
The Alkaloids: Chemistry and Pharmacology

# data[].attributes.description
The Alkaloids: Chemistry and Pharmacology