Wolfram Mathematica® provides a collection of ready to use functions, and with its rules of programming it sets the stage like a chess board. Now it depends on you (and your imagination) how to combine these and make your move to attack the problem in hand. It always helps to look at different resources to get ideas of ways to combine the Mathematica functions. There are excellent books written about Mathematica, for example Ilan Vardi [5], Stan Wagon [6], Shaw–Tigg [4] and Gaylord, Kamin, Wellin [2]to name a few. The reader is encouraged to have a look at them. Wolfram demonstration projects http://demonstrations.wolfram.com/ contains many interesting examples of how to use Mathematica in different disciplines. And finally, the Mathematica Help and its virtual book is a treasure, dig it!

R. Hazrat, Mathematica ®: A Problem-Centered Approach, Springer Undergraduate Mathematics Series, DOI 10.1007/978-1-84996-251-3, © Springer-Verlag London Limited 2010 Bibliography

[1] R. Gaylord, Mathematica Programming Fundamentals, Lecture Notes, Available in MathSource 100 [2] R. Gaylord, S. Kamin, P. Wellin, An introduction to programming with Mathematica, Cambridge University Press, 2005. 146, 184 [3] S. Rabinowitz, Index to Mathematical problems 1980–1984, Math pro Press. 1992. viii [4] W. Shaw, J. Tigg, Applied Mathematica, Addison-Wesley Publishing, 1994. 184 [5] I. Vardi, Computational Recreations in Mathematica, Addison-Wesley Pub- lishing, 1991. 62, 92, 184 [6] S. Wagon, Mathematica in Action, Springer-Verlag, 1999. 146, 184 [7] E. Weisstein, MathWorld, http://mathworld.wolfram.com/. 53

R. Hazrat, Mathematica ®: A Problem-Centered Approach, Springer Undergraduate Mathematics Series, DOI 10.1007/978-1-84996-251-3, © Springer-Verlag London Limited 2010 Index

Abs,62 Degree,12 Accumulate,91 Delete,28 Algebraic,56 derivation, 163 Alt+., 9 Det, 129 And,55 DictionaryLookup,43 anonymous function, 23 Divisible,23 Apart,10 Divisor,39 Append, 28, 59 Divisors,51 AppendTo,59 Do,72 Apply, 48, 108 Dot, 129 Array, 129 Drop,26 AxesStyle, 142 Dynamic,16 dynamic variable, 15 Background, 142 D[], 163 BarChart, 31, 44 Binomial,8 Eigenvalues, 134 Block, 118 Eigenvectors, 134 Boolean expression, 54 EvenQ,36 Boolean function, 35 Exist,57 Booleans,56 Expand,9

Cases, 102 Factor,9 Clear,13 FactorInteger,6 Cmd+., 9 Fibonacci,21 Coefficient,71 Fibonacci number, 21 CoefficientList,68 FillingStyle, 142 Complement,59 FindInstance, 158 Complexes,56 FindRoot, 158 ContourPlot, 135 First,26 ContourPlot3D, 153 FixedPointList,87 Count, 171 Flatten, 27, 83 Fold,90 deﬁning variables, 12 FoldList, 90, 146

R. Hazrat, Mathematica ®: A Problem-Centered Approach, Springer Undergraduate Mathematics Series, DOI 10.1007/978-1-84996-251-3, © Springer-Verlag London Limited 2010 Index 187

For,78 Map, 33, 107 ForAll,57 MatchQ, 100 Frame, 142 matrix, 128 FrameLabel, 142 MatrixForm, 129 FrameStyle, 142 Maximize, 166 FromDigits,37 MaxIterations,97 FullForm,47 MaxRecursive, 145 FullSimplify,4 MemberQ, 78, 105 function, 19 Min,52 – multi def’s., 113 Minimize, 166 – with condition, 112 Mod,8 Module, 118 Graphics, 147 Most,26 graphics, 135 GraphicsColumn, 145 N,3 GraphicsGrid, 145, 150 NestList,84 GraphicsRow, 145 NestWhile,86 GraphPlot,94 NestWhileList,86 Next,84 Head,48 NIntegrate, 163 NMaximize, 166 If,61 NMinimize, 166 if statement, 61 Norm, 127 Implies,57 Not,55 Inner,93 NProduct,71 inner product, 127 NSolve, 158 Input,77 NSum,69 Insert,28 IntegerDigits,37 IntegerExponent, 111 OddQ,36 IntegerQ,36 Or,55 Integers,56 Outer, 56, 93 Integrate, 163 integration, 163 palindromic, 43 Intersection,58 ParametrixPlot, 135 Inverse, 129 ParametrixPlot3D, 153 Partition, 177 Join,60 pattern matching, 100 perfect number, 51 Last,26 Permutations,98 Length,35 Piecewise, 63, 143 LengthWhile,89 Plot, 135 Line, 147 Plot3D, 153 list, 25 PlotPoints, 145 listable function, 32 PlotStyle, 142 ListAnimate, 154 PolarPlot, 135 ListPlot, 149 Prepend,28 loop, 72 Prime,6 – Do-loop, 72 prime number, 2 – For-loop, 78 PrimePi,7 –nestedloop,81 Primes,56 – While-loop, 75 Print,30 Product,70 Manipulate,17 pure function, 23 188 Index

Quiet,97 StringLength,45 quit kernel, 9 StringReplace,45 Quotient,9,87 StringReverse, 43, 44 StringTake,45 RandomInteger,34 sublime number, 53 Range,28 Sum,65 Rationals,56 RealDigits, 146 Table, 28, 83 Reals,56 Take,26 RecursionLimit, 123 TakeWhile,89 Reduce, 158 Tally,60 RegionPlot, 135 Thread,52 RegionPlot3D, 153 three-dimensional graph, 153 ReplaceAll,97 Thue-Morse seq., 98, 151 ReplaceList, 107 Timing,73 ReplaceRepeated,97 Together,10 Rest,26 ToString,45 Reverse, 28, 37 Transpose,93 RotateLeft,28 TreeForm,49 RotateRight,28 TrigExpand,11 rules, 96 TrigFactor,11 two-dimensional graph, 135 Select, 34, 41 Short,45 Show, 141 Union, 40, 58 Simplify,4 Slider,16 vector, 127 social number, 90 Solve, 158 weird number, 53 solving equation, 158 Which,61 Sort,28 which statement, 61 square free, 41 While,75 StringDrop,45 With, 118

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