Mathematics Geometry Form 1: Fill & Download for Free

The principle of simple common sense is not accepted in Mathematics because:There is no such principle;If you can formalise such a principle it would be accepted;Simple common sense is neither simple nor particularly common; andAttempts to formalise such a principle lead to paradox, inconsistency, and confusion.Not only that but there are endless examples where common sense is usefully violated including:Non-Euclidean geometry[1];Square roots of negative numbers[2]; andOne-to-one correspondence between elements of a set and a proper subset of the set[3].I might even argue that Mathematics is the subject where rigour and precision trump common sense. Other subjects can perhaps get away with common sense, but in Mathematics it is a positive pleasure to challenge common sense [math]\ddot\smallsmile[/math]Footnotes[1] Non-Euclidean geometry - Wikipedia[2] Imaginary number - Wikipedia[3] Cardinality - Wikipedia

Thanks for the A2A.I’ll take this to mean obscure uses in mathematics :). These are just neat things that sometimes aren’t covered in a topology course and I would like to know more about. I know that the geometry ones are less obscure.In Algebra:Proof of Cayley-Hamilton via Zariski denseness. The idea is to prove the theorem for linear maps with distinct eigenvalues (these are diagonalizable.) Observe that the theorem is true here, and that the space of matrices with the same eigenvalue correspond to the vanishing locus of the discriminant of the characteristic polynomial. Hence, the statement is true in the general case by continuity (in the Zariski topology.)Proof of Bezout’s theorem via simple closed curves. This takes some work (classification of surfaces, mapping class group of torus.)Proof of the fundamental theorem of algebra using the Lefschetz fixed point theorem on the sphere.Nielsen Schreier- (subgroup of a free group is free.)In Geometry(cheat) vanishing of vector fields by characteristic classes (in particular the celebrated “hairy ball theorem.”solutions to all sorts of enumeration problems by studying cohomology classes via geometric cup product (intersection)http://www.math.colostate.edu/~renzo/UCR1.pdfApplications to discrete geometry/ topological combinatorics (Ham-sandwich theorem and discrete analogues) by equivariant topology. http://people.mpim-bonn.mpg.de/matschke/thesisMatschke.pdfStudying complex dynamics by “moduli space” of polynomials and its topology (Mandelbrot set and quadratic polynomials!)

Hi!My personal favourite books for Mathematics are;• Mathematics: Maths XI & XII by R.D. Sharma• Trigonometry & Geometry : 1. Plane Trigonometry Part 1 by S.L. Loney 2. Plane Co-ordinate Geometry by S.L. Loney• Algebra : Higher Algebra by Hall and Knight• Calculus : Problems in Calculus of One Variable by I.A. MaronYou can get all of them free of cost. Visit our website MyPustak and place the order.Thank you!!