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Free Term Papers - Mathematics Term Papers

Abstract Algebra: Groups

Q1.consider the rotation of an equilateral triangle under the operation (rotation by 120 degrees)where A = position 1 B = position 2 C = position 3 after 1 turn of 120 degrees A moves to position 2 and after 2 turns of 120 degrees A is then in position 3. If I is the starting position,R1 represents the position after 1 rotation of 120 degrees and R2 represents the position after 2 rotations of 120 degrees. Is ({I,R1,R2}) a group? Clearly state the identity and give the inverse of each element if applicable. Q2. a number is divisible by 9 if and only if the sum of its digits is also divisible by 9.prove this test for divisibility by 9 with three digit numbers and extend the idea to numbers with more digits.

Excerpt: "i.e. a1+a2+a3+a4+a5=9(k-1111*a1+111*a2+11*a3+a4 The above shows that a five digits number is divisible by 9 if and only if the sum of its digits is divisible by 9, and can easily be extend to a number with six digits and more."

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Pure Maths: Sequences and Series

[...]The table shows the formula for values of n from 1 to 10, with corresponding multiples of 5 from 5 to 50 inclusive.[...]

Excerpt: "It is often easier to explain results to people graphically, particularly if the recipient doesn't have a strong maths background. Also if the relationship is not obvious then investigation graphically with techniques such as scatter graphs will often be useful. However, there are many situations where the analysis does not lend itself to graphical analysis, for example when trying to explore the relationship between a variable and several others upon which it depends."

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