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Advanced problems in mathematics preparing for university New revised Edition by Stephen Siklos ISBN 9781783747764 1783747765

Name: Advanced problems in mathematics preparing for university New revised Edition by Stephen Siklos ISBN 9781783747764 1783747765
SKU: EB-32860810
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Advanced problems in mathematics preparing for university Stephen Siklos Digital Instant Download

Author(s): Stephen Siklos

ISBN(s): 9781783747764, 9781783747771, 1783747765, 1783747773

Edition: New revised

File Details: PDF, 7.44 MB

Year: 2019

Language: English

SKU: EB-32860810 Category: Mathematics - Mathematical Foundations Tag: Stephen Siklos

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Advanced problems in mathematics preparing for university New revised Edition by Stephen Siklos – Ebook PDF Instant Download/Delivery: 9781783747764 ,1783747765
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ISBN 10: 1783747765
ISBN 13: 9781783747764
Author: Stephen Siklos

This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics. “This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

Advanced problems in mathematics preparing for university New revised Edition Table of contents:

Problem 1: An integer equation
Problem 2: Partitions of 10 and 20
Problem 3: Mathematical deduction
Problem 4: Divisibility
Problem 5: The modulus function
Problem 6: The regular Reuleaux heptagon
Problem 7: Chain of equations
Problem 8: Trig. equations
Problem 9: Integration by substitution
Problem 10: True or false
Problem 11: Egyptian fractions
Problem 12: Maximising with constraints
Problem 13: Binomial expansion
Problem 14: Sketching subsets of the plane
Problem 15: More sketching subsets of the plane
Problem 16: Non-linear simultaneous equations
Problem 17: Inequalities
Problem 18: Inequalities from cubics
Problem 19: Logarithms
Problem 20: Cosmological models
Problem 21: Melting snowballs
Problem 22: Gregory’s series
Problem 23: Intersection of ellipses
Problem 24: Sketching x^m(1 – x)^n
Problem 25: Inequalities by area estimates
Problem 26: Simultaneous integral equations
Problem 27: Relation between coefficients of quartic for real roots
Problem 28: Fermat numbers
Problem 29: Telescoping series
Problem 30: Integer solutions of cubics
Problem 31: The harmonic series
Problem 32: Integration by substitution
Problem 33: More curve sketching
Problem 34: Trig. sum
Problem 35: Roots of a cubic equation
Problem 36: Root counting
Problem 37: Irrationality of e
Problem 38: Discontinuous integrands
Problem 39: A difficult integral
Problem 40: Estimating the value of an integral
Problem 41: Integrating the modulus function
Problem 42: Geometry
Problem 43: The t substitution
Problem 44: A differential-difference equation
Problem 45: Lagrange’s identity
Problem 46: Bernoulli polynomials
Problem 47: Vector geometry
Problem 48: Solving a quartic
Problem 49: Areas and volumes
Problem 50: More curve sketching
Problem 51: Spherical loaf
Problem 52: Snowploughing
Problem 53: Tortoise and hare
Problem 54: How did the chicken cross the road?
Problem 55: Hank’s gold mine
Problem 56: A chocolate orange
Problem 57: Lorry on bend
Problem 58: Fielding
Problem 59: Equilibrium of rod of non-uniform density
Problem 60: Newton’s cradle
Problem 61: Kinematics of rotating target
Problem 62: Particle on wedge
Problem 63: Sphere on step
Problem 64: Elastic band on cylinder
Problem 65: A knock-out tournament
Problem 66: Harry the calculating horse
Problem 67: PIN guessing
Problem 68: Breaking plates
Problem 69: Lottery
Problem 70: Bodies in the fridge
Problem 71: Choosing keys
Problem 72: Commuting by train
Problem 73: Collecting voles
Problem 74: Breaking a stick
Problem 75: Random quadratics
Syllabus

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Tags: Stephen Siklos, Advanced problems, mathematics, university