Number Theory: An Overview for Beginners

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Number theory is a branch of mathematics focused on the properties and relationships of numbers, particularly integers. It encompasses concepts such as modular arithmetic, the Euclidean algorithm, and divisibility properties, which are essential for advanced mathematical proofs. The Chinese remainder theorem is also a significant tool within this field. For beginners, reading a book on elementary number theory is recommended to build foundational knowledge. Understanding these concepts can enhance skills in various areas of mathematics.
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what exactly is numder theory i have heard of it but i don't know what it is
 
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http://en.wikipedia.org/wiki/Number_theory

Reading a book on Elementary number theory would be advisable if you are getting into advanced mathematics, or even if you are just curious about it. Modular arithmetic, the Euclidean algorithm, divisibility properties, and the Chinese remainder theorem are all good tools to use in proofs in other math courses.
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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