Journey Into Mathematics : An Introduction to Proofs

Preface vii To the Reader xi To the Instructor xiii Setting Out 1(30) Induction 1(21) Binomial Coefficients 22(9) Things Pythagorean 31(67) Area 31(14) The Pythagorean Theorem 45(11) Pythagorean Triples 56(8) The Method of Diophantus 64(8) Trigonometry 72(14) Integration 86(12) Circles and π 98(51) Approximations 98(9) The Area of a Disk 107(10) The Circumference of a Disk 117(17) Sequences 134(15) Polynomials 149(64) Quadratics 149(11) Complex Numbers 160(11) De Moivre's Theorem 171(12) Cubics and Quartics 183(21) Irrationalities 204(9) Epilogue 213(2) Bibliography 215(2) Glossary of Logic 217(16) Propositional Calculus 217(5) Proofs 222(2) Set Theory 224(4) Quantifiers 228(5) Index 233