The Stanford Mathematics Problem Book: With Hints and Solutions
This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers high school and college students an excellent mathematics workbook of rigorous problems that will assist in developing and cultivating their logic and probability skills.These 20 sets of intriguing problems test originality and insight rather than routine competence. They involve theorizing and verifying mathematical facts; examining the results of general statements; discovering that highly plausible conjectures can be incorrect; solving sequences of subproblems to reveal theory construction; and recognizing "red herrings," in which obvious relationships among the data prove irrelevant to solutions. Hints for each problem appear in a separate section, and a final section features solutions that outline the appropriate procedures.Ideal for teachers seeking challenging practice math problems for their gifted students, this book will also help students prepare for mathematics, science, and engineering programs. Mathematics buffs of all ages will also find it a source of captivating challenges.
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accessible related problem altitude angle arithmetic progression CALCULUS OF VARIATIONS California Mathematics Council cents circle circumscribed condition congruent DIFFERENTIAL EQUATIONS Discovery by induction distance divisible Draw a ﬁgure edge equal equation yields equilateral triangles Examination in Mathematics ﬁnal term ﬁnd ﬁve FOURIER SERIES frustum given triangle guess Hence hexagon HINTS hypotenuse induction needs observation inscribed integers intersection Introduce suitable notation INTRODUCTION isosceles triangle key plane ﬁgure know a related law of cosines law of sines left-hand sides line segments mathematical induction Mathematical Monthly Mathematics Council Bulletin matical obtain octahedron opposite ORDINARY DIFFERENTIAL EQUATIONS perpendicular points polygon polynomial prism Propositions Prove your answer pyramid quadrilateral radius ratio rectangle regular tetrahedron respectively restate the problem right prism right triangle right-hand side Separate the various side of length Solve Stanford University Competitive symmetric text covers theory three equations University Competitive Examination vertex vertices volume