objectives_1 - A Course On Computing For Computing Student...

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A C ourse O n C omputing F or C omputing S tudent L earning O bjective 1 1 A learning objective is something a student will understand and be able to continually use. William Shoaff January 5 , 2010 Text in blue jump to a section in the textbook where the topic is presented. Text in green jump to an external Web page, often Wikipedia . Name, Values, and Types: A name is a string over a finite alphabet . The name is used to write, pronounce, or call the value of some- thing. Values can be organized into types where useful operations and functions can be computed. Alphabets: List several instances of an alphabet . B , D , H , E Strings: The set of all strings over an alphabet can be defined recursively: The empty string λ is a string; Each character c in the alphabet is a string; If s and t are strings then st is a string; Nothing else is a string. Types: A type is a set of values named by strings over a finite alphabet. Number Systems: A number system is a type for expressing numeric values and operations on them. Natural Numbers : The set N of discrete values { 0, 1, 2, . . . } with addition and multiplication. Integers : The set Z of discrete values { 0, ± 1, ± 2, . . . } with addition, subtraction, and multiplication. Rationals : The set Q of discrete values { a / b : a , b Z b 6 = 0 } with addition, subtraction, multiplication, and division. Reals : The R is an uncountable set of continuous values that can defined using notions from mathematical analysis. Bases 2 , 10 and 16 : Common alphabets used for naming numeric values. Conversion Algorithms for Natural Numbers: Convert between names for the same value written in different languages Horner’s Rule : Use Horner’s rule to convert from binary or hexadecimal to decimal Remaindering : Use repeated remaindering to convert from decimal to binary or hexadecimal Integers Encodings: There are multiple methods to encode inte- gers Sign-Magnitude Place an explicit plus + or minus - symbol before the number + = 1 and - = 0 in binary. Complement Notation represents positive and negative inte- gers. Use complement and convert between it and decimal signed-magnitude notation
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a course on computing for computing student learning objective 2 Biased Notation Interpret the value of number written in bi- ased notation . Floating Point Interpret the value of a number written in floating point notation . Data Structures A data structure organizes information for efficient processing. Sets A set is an unordered collection. Element Of Given a set X and an element x , compute the Boolean function ElementOf ( x , X ) If there is an algorithm for this function, the set X is decidable. Otherwise, x X is undecidable. Subset Of Given a sets A and B , compute the Boolean func- tion SubsetOf ( A , B ) Empty Set There is one empty set with no elements.
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