A Course in Python: The Core of the Language (Springer Undergraduate Mathematics Series)

Preface....6 Contents....8 Chapter 1 Basics of Python....10 1.1 Basic Arithmetic....10 1.2 Integers, Reals and Complex Numbers....13 1.3 Objects and their Types....19 1.4 Importing Libraries in Python....22 1.5 Variables in Python....23 1.6 Equalities and Boolean Statements....24 1.7 Strings....27 1.8 Strings as Objects....28 1.9 Input and Output....29 Problems....31 Chapter 2 Lists and Tuples....32 2.1 Data: Lists....32 2.1.1 Accessing entries of a list....33 2.2 Lists as Objects....38 2.3 A First Glimpse of Graphics....47 2.4 A First Glimpse of Importing Data....48 2.5 Tuples....50 2.6 More Examples of Working with Data....51 2.6.1 Languages....51 Problems....55 Chapter 3 Decisions and Repetitions....57 3.1 Decision Making: The Fork on the Road....57 3.2 Decision Making: The Forks on the Road....60 3.3 Loops and Repetitions....64 3.3.1 For-loop....64 3.3.2 Nested For-loops....79 3.3.3 While Loops....84 Problems....89 Chapter 4 Functions....92 4.1 Functions....92 4.1.1 The scope of functions....96 4.1.2 Functions, default values....108 4.1.3 Functions, specific types....109 4.2 Functional Programming: Anonymous (lambda) Functions....110 4.2.1 Selecting from a collection....117 4.2.2 Functional programming, reduce....120 Problems....126 Chapter 5 List Comprehension and Generators....129 5.1 List Comprehension....129 5.1.1 Putting conditions on parameters....131 5.2 Sets and Dictionaries....137 5.2.1 Sets....137 5.2.2 Dictionaries....145 5.3 Generators....150 5.3.1 Generator functions....153 Problems....156 Chapter 6 The sympy Library....159 6.1 sympy, Symbolic Python....159 6.2 Graphics in sympy....164 6.3 Three-Dimensional Graphs....171 6.4 Calculus with sympy....176 6.4.1 Solving equations....176 6.4.2 Limits, derivation and integration....179 Problems....186 Chapter 7 The numpy Library....189 7.1 numpy, Numerical Python....189 7.1.1 Calculus on arrays....190 7.1.2 Generating arrays....191 7.1.3 Accessing entries of an array....193 7.1.4 Vector calculus with arrays....199 7.2 Universal Functions....213 Problems....214 Chapter 8 The matplotlib Library and Projects....216 8.1 matplotlib, Plotting Data....216 8.2 Plots as Objects....223 8.3 Animation....227 8.4 Case Study, Persian Carpets....233 8.5 Case Study, Predictive Estimation....239 8.6 Case Study, the Thue–Morse Sequence....247 Problems....249 Further Reading....252 Index....254