Mathematics for Computer Scientists
A Practice-Oriented Approach
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Chapter
Appendix
In the appendix you will find the Greek alphabet as well as the table of the normal distribution.
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Chapter
Dot Product and Orthogonal Map**s
In this chapter you will learn:
the dot product and norms for real vector spaces,
the special dot product in
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Chapter
Sets and Map**s
Sets, operations on sets and map**s between sets are part of the language of mathematics. Therefore, we begin the book with them. If you have worked through this first chapter, you will know
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Chapter
The Real Numbers
This chapter lays the foundation for investigations of convergent sequences and continuous functions. By the end of this chapter, you will
know what characterizes the real numbers,
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Book
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Chapter
Natural Numbers, Mathematical Induction, Recursion
At the end of this chapter
you will know what an axiomatic system is, and know the axioms of natural numbers,
you can represent natural...
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Chapter
Continuous Functions
The study of continuous functions is at the center of analysis. If you have worked through this chapter
you know what a continuous real or complex function is and can check if a giv...
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Chapter
Algebraic Structures
At the end of this chapter
you will know what an algebraic structure is,
you will know the most important algebraic structures: groups,...
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Chapter
Integral Calculus
At the end of this chapter you will have
learned the integral as the area under a piecewise continuous function,
understood the connect...
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Chapter
Random Variables
After finishing this chapter
you will know what discrete and continuous random variables are,
you will know the connection between rand...
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Chapter
Matrices
The use of coordinates and matrices in linear algebra lays the foundation for algorithms in many areas of computer science. By the end of this chapter, you will know
the relation be...
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Chapter
Numerical Methods
The final chapter from the second part of the book familiarizes you with applications of theoretical mathematics to specific computational tasks. At the end of this chapter
you kno...
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Chapter
Statistical Methods
Now you can reap the fruits of the last chapters. If you have worked through this chapter
then you know what a sample is, and can calculate the sample mean, the mean squared error a...
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Chapter
Eigenvalues, Eigenvectors and Change of Basis
At the end of this chapter
you will know what the determinant of a matrix is and can compute it,
you have learned the terms eigenvalue ...
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Chapter
Graph Theory
This chapter contains many algorithms and is particularly close to computer science. If you have worked through it
you know the basic concepts of graph theory: nodes, edges, degree,...
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Chapter
Logic
As a computer scientist you are constantly dealing with tasks from logic. In this chapter you will learn
what a proposition is,
the dif...
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Chapter
Sequences and Series
At the end of this chapter
you will know what convergent sequences are, and be able to calculate limits of sequences,
you will be able ...
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Chapter
Some Number Theory
The central learning content of this chapter is
the binomial coefficient and its most important properties,
the use of the mathematical...
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Chapter
Differential Calculus
A long chapter lies before you. If you manage it
you know the definition of the derivative for functions of one or more variables,
you ...
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Chapter
Vector Spaces
In this chapter you will learn
the operations on the classical vector spaces \({\mathbb{R}}^{2}\) ...
