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Coin tosses, 124 Markov chains and, 153 Pascal s triangle and, 129 Coloring problems, 172 178 Columns, of matrices, 136 Combinatorial theory, 130 Complements, 45 Complete induction, 36 Complex conjugate, 99 Complex numbers (C), 52 Composition, matrices and, 136 Compound connectives, 7, 12 16 Computers, Alan Turing and, 201, 203 Computer science, 196 Conclusion, 8 Condensed series, 280 Conjunction, 4 Connectives, 1, 3 16 Constant coef cient, 63 Contradiction, proof by, 29 32 Contrapositive, 12 16 Convergence, 261, 269 288 of p-series, 279 282, 286, 291 sequences and, 250 test for, 269, 283 288 Converse, 12 16 Cosets, 191, 224 Counting arguments, 105 134 Counting numbers, 51 Cryptoanalysis, 208 Cryptography, 199, 203 209 See also Encryption Alan Turing and, 199 Fermat theorems and, 196 Cryptosystems, 204, 207

When users decide to fill out a form, such as the one shown in Figure 14-1, they click inside a field with the Hand tool When the user clicks inside the form field, the cursor becomes an I-beam indicating that data can be entered from the user s keyboard To navigate to another field, the user can either click inside another field with the selected Hand tool or press TAB to advance to the next field The user can correct an entry error by clicking inside the field with the Hand tool, clicking and dragging to select a word or letter that needs to be changed, and then entering

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Edges, 165 167, 169 Element of, 41 Elementary statement, 1 Elements, of matrices, 136 Empty sets, 44 Enciphering, 204 Encoding, 204, 235 Encryption, 204 af ne transformations and, 209 216 digraph transformations and, 217 221 RSA, 221 233 Engineering, 3 complex numbers and, 52 group theory and, 196 matrices and, 135 Enigma machine, 203 Equivalence classes, 54, 192 integers and, 73 75 rational numbers and, 79 81 Equivalence relations, 54, 95, 191 Equivalent modulo, 186 Euclid s theorems, prime numbers and, 185 Euclidean algorithm, 184, 211 Euclidean plane, complex numbers and, 97 Euler, Leonhard, 163 Euler characteristic, 167 Euler paths, 170 Euler s theory/formula, 163 168 Even integers, 54 Even natural numbers, 24 Exam questions, 301 323 Exclusive or, 4, 44 Exercises boolean algebra, 241 counting, 132 encryption/decryption, 233 functions, 65 logic, 20 matrices, 161 numbers, 102, 197 proof, 40

FIGURE 14-1

Dantzig s method of linear programming, 156, 158 Decimal expansions, 52 Decimals, in nitely repeating, 266 268 Deciphering, 204 Decrypting messages, 208 214, 219 222 Dedekind, Julius W R, 91 Dedekind method, 91 De-encrypting, 204 De nitions, 2, 23, 42 De Morgan, Augustus, 172 de Morgan s laws, 8, 46 Digraphs, 216 221 Direct proof, 24 29 Dirichlet, Gustav Lejeune, 32 Dirichlet s drawer-shutting principle, 105 108 Dirichletscher Schubfachschluss, 32, 105 108

the new data If the form is equipped with a properly programmed Reset button, the user can start over by clicking the button

relations, 65 sequences, 256 series, 298 set theory, 49 solutions/answers to, 325 346 Exponential functions, 63 Exponentiation, 48 Greatest lower bounds, 87 Greedy algorithm, 180 Group of order 6, 193 Group of order m, 194 Groups, 187 196 isomorphism of, 194 196 linear, 188 noncommutative, 189 of order 6, 193 of order m, 194 subgroups and, 190 Guthrie, Francis W, 172

You use a tool from the Forms toolbar or choose Tools | Advanced Editing | Forms and then choose the desired tool to create fields in your PDF forms Your choice of tool specifies what the field does or what type of data it accepts You can assign actions to form fields to create a desired result when a user interacts with the form field In Acrobat Professional, you can create any of the following types of form fields:

Faces (regions), 165 False/true, 2, 29 Feasible region, 157 160 de Fermat, Pierre, 178, 196 Fermat s theorems, 196, 224, 228 Fibonacci sequence, 118 Fields, 82 Filters, 94 Final exam, 301 323 Finite intersection property, 94 Finite ordinal arithmetic, 69 First-order logic, 19 for all ( ), 2, 16 19 Formal mathematical statements, 25 Four-color problem, 172 178 Fractions, 52, 266 Frequency analysis, 208 Functional composition, 60 Functions, 56 66 combining, 59 63 exponential, 63 inverse, 61 logarithmic, 64 polynomial, 63 relations and, 53 55 types of, 63 65 Fundamental theorem of arithmetic, 185

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