TO: M.S. Students in Computer Science Studying at the Coral Gables Campus FROM: Comprehensive Examinations Committee DATE: February 23, 1995
Comprehensive exams will test general knowledge in computer science -- the knowledge every computer scientist is expected to possess. The questions in the comprehensive exams will concern important ideas, not technical details. Although certain computer science courses are recommended as helpful in preparing for the comprehensive exams, the questions asked will differ in character from the questions from corresponding final exams. An old proverb says one cannot see the forest for the trees; in a comprehensive exam the students are expected to show that this is not the case for their understanding of computer science.
Students can prepare for comprehensive exams by taking courses and/or by individual study. Normal course selection will prepare the student adequately for the Core Comprehensive Exam. However the student must be careful to select appropriate courses to prepare for the Advanced Comprehensive Exams. Course sequences are highly recommended to establish the concentration required for success in the Advanced Exams.
A student who chooses the Non-Thesis Option is required to pass the the Core Comprehensive Exam and two Advanced Comprehensive Exams.
The Core Comprehensive Exam covers the material required for a B.S. in Computer Science and additional topics specified by the Curriculum Committee. These topics are essential to every computer scientist, independently of the specialization.
Each Advanced Comprehensive Exam corresponds to a possible specialization offered by the department's computer science curriculum at the M.S. level. The Advanced Comprehensive Exams must be chosen from the list prepared for the given semester by the Curriculum Committee.
Detailed list of topics for the Core Exam is available. (The list may undergo slight adjustments from one semester to another, so please make sure that you are using the current list.) The list includes references to literature. The books which are quoted are not required, there are other sources of the same information.
It is not necessary to pass an examination at the first attempt. Nor is it necessary to take the exams in the same semester. (The Comprehensive Exams are offered once in the fall semester and once on the spring semester.)
CORE EXAM TOPICS Basic programming methodology modularity structured programming abstract data types pre-conditions, post-conditions, loop invariants recursion vs. iteration Fundamental data structures [CLR] or [AHU] linked lists heaps trees Fundamental abstract data types and their implementations [CLR] or [AHU] lists sets stacks queues, priority queues tables Fundamental algorithms [CLR] or [AHU] sorting selection-sort insertion-sort radix-sort (bin-sort) quick-sort merge-sort heap-sort tree-sort searching search trees binary search self-balancing trees, e.g. AVL and 2-3 trees hashing conflict resolution hash functions basic graph algorithms tree traversals minimum weight spanning tree shortest path depth first search breadth-first search topological sorting strongly connected components Basic algorithm analysis [CLR] or [AHU] the big O and Omega notation worst case and average case analysis solving simple recurrence relations efficiency of the algorithms above computing efficiency of other algorithms Problem solving strategies [AHU] divide and conquer dynamic programming greedy algorithms backtracking local search (local optimization, hill climbing) Fundamentals of computer architecture and logic design [M] design of logic components combinatorial logic sequential logic components of the CPU interrupts caching direct memory access principles of assembly language programming Fundamentals of operating systems [PS] kernel semaphores, monitors, etc. interprocess communication file systems scheduling memory management deadlock protection Basic theory of programming languages [FG] identifier binding, scope and range, parameter passing scoping and block structure activation record structure recursion static links, nested procedures co-routines, etc. syntax and translation implementation of abstraction and encapsulation Fundamentals of databases [EN] DBMS vs. file processing systems catalog three-level architecture access methods for files sequential search binary search external hashing indices: primary, clustered, secondary, multilevel, B+ trees operations on files double buffering entity-relationship diagram relational model relational algebra and calculus constraints mapping from the ER-diagram querying a relational database, e.g. in SQL Basic discrete mathematics [Rm] induction relations and partially ordered sets elements of propositional logic Boolean expressions vs. truth tables Boolean expressions vs. circuits combinatorics and counting countable and uncountable sets propositional logic basic graph theory generating functions Basic probability theory [Rs] sample space and probability conditional probability and Bayes Theorem independent events random variables expected value and variance probability distributions discrete: hypergeometric, binomial, Poisson continuous: uniform, exponential, normal, normal approximation to binomial Vectors and matrices [S] vector spaces and linear independence scalar product matrix multiplication and inversion determinants solving a system of n linear equations with m variables Basic automata theory [LP] deterministic and nondeterministic finite automata regular expressions context-free grammars and BNF deterministic and nondeterministic Turing machines recursive sets non-recursive sets: halting problem r.e sets computational time/space complexity, P and NP RELEVANT COURSES MTH210 Vectors and Matrices, MTH220 Programming II, MTH224 Probability, EEN228 Assembly Languages, EEN304 Logic Design, MTH309 Discrete Math, MTH322 Unix and C, EEN414 Computer Architecture, MTH517 Data Structures, MTH519 Theory of Programming Languages, MTH596 or EEN521 Operating Systems, MTH523 Databases, MTH527 Automata and Formal Languages, REFERENCES [AHU] A. Aho, J. Hopcroft and J. Ullman, Data Structures and Algorithms, Addison-Wesley, 1983. [CLR] T. Cormen, Ch. Leiserson, R Rivest Introduction to Algorithms MIT Press, 1990 [EN] Elmasri and Navathe Fundamentals of Database Systems Second Edition Benjamin/Cummings Publishing Co., 1994. [FG] Fisher and Grodzinsky The Anatomy of Programming Language Prentice Hall [LP] H. Lewis and C. Papadimitriou, Elements of the Theory of Computation, Prentice-Hall, 1981. [M] M. Mano, Digital Design, Prentice-Hall, 1984. [PS] J. Peterson, A. Silbershatz, Operating System Concepts, third edition, Addison-Wesley, 1991. [Rm] S. Roman, An Introduction to Discrete Mathematics, Harcourt Brace and Jovanovich, 1989. [Rs] S. Ross A First Course in Probability Third Edition Collier Macmillian Publishers, 1988. relevant sections from chapters 1-5, 7. [S] Introduction to Linear Algebra Strang Wellesley Cambridge Press