BSC Mathematics Notes

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Algebra I

Total Marks: 100
Theory: 75
Internal Assessment: 25
5 Lectures, 1 Tutorial (per week per student)

Polar representation of complex numbers, the nth root of unity, some simple geometric notions and properties, conditions in collinearity, orthogonality and concyclicity, similar triangles, equilateral triangles, some analytic geometry in the complex plane, the circle, statement of the fundamental theorem of algebra and its consequences, Descartes’ rule of signs, bound on the real zeros, interpreting the coefficients of a polynomial.
References:
[1]: Chapter 2, Chapter 3.
[2]: Chapter 4 (Sections 4.4, 4.6 (4.6.1-4.6.8)), Chapter 5 (Sections 5.2.7, 5.2.12),
Chapter 6 (Section 6.1)
Sets, binary relations, equivalence relations, congruence relation between integers, finite product of sets, functions, composition of functions, bijective functions, invertible functions, introduction of finite and infinite sets through correspondence, binary operations, principle of mathematical induction, well-ordering property of positive integers, division algorithm, statement of fundamental theorem of arithmetic.

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