Description:
This Honors course is a fully-interactive programming course for high school students that teaches the programming language Scheme; this is the language of choice at many computer science universities in the world. The course is built to take advantage of the latest Internet browser technology. The course presents a carefully-crafted and thoroughly field-tested development of the material and features of online Scheme interpreter, automatic grading of student programs, an integrated help forum, and teacher tools for tracking student progress.

This course takes advantage of the simple and elegant structure of Scheme, which allows students to focus on computer science concepts (such as functional programming, recursion, data structures, and object-oriented programming) rather than the frustrating details of a particular language. It introduces students to the algorithmic process by first diagramming operations in an organized manner before tackling the code syntax.

Advanced material covered in this course includes Boolean arithmetic and truth tables, recursion, numeric algorithms (from a simple number-theoretic perspective), data structures (lists, arrays, and trees), object-oriented programming, and functional programming. Although covering such advanced topics, the course is written in a style and at a level that is easily understood by high school students. Students completing this course will have the computer science background to embark with confidence into the Advanced Placement Computer Science course.

Description:
This AP course is a computer science course leading to the Advanced Placement Computer Science exam. The course can be completed in eight months, allowing students time to review for and take the AP exam itself. The curriculum is presented on web pages in which Java compilers are embedded at key points. The course covers both the A and AB exams.

All students take the A segment of the course. More advanced students may also take the AB segment to prepare for the AB exam. Interspersed within a well-organized exposition are exercises to be completed using the embedded compiler and tests that are graded automatically.

AP Computer Science makes use of a web service to embed a Java compiler directly into interactive web pages. The authors use this technology to reveal only those code segments that are immediately relevant to the student. The resulting programs can be executed online with the press of a button. The advantage offered by this technology is huge. Beginning students can write and test simple programs immediately. In addition, the interactive web pages include a Java "single step debugger," which students use to single step through programs observing the flow of control and changing variable values.

Description:
Introduction to Logic I: The Propositional Calculus

This honors course introduces students to the propositional calculus: well-formed formulas; negation, conjunction, disjunction, implication, and equivalence; truth tables; tautologies and contradictions; the tautology principle; Modus Ponens, conjunctive inference and conjunctive simplification, contra positive inference and Modus Tollens, syllogistic inference and inference by cases; the substitution principle; and the Deduction Theorem and the Principle of Indirect Inference. The object language/metalanguage distinction is also discussed.

Description:
This honors course introduces students to the predicate calculus (with equality); terms and formulas; free and bound occurrences of variables; open and closed terms and formulas; metaterms and metaformulas; tautologies; axioms for the predicate calculus; demonstrations; universal and existential quantification and the related inference schemes; theorems and metatheorems and their use in demonstrations; and the substitution principle.

Description:
This honors course introduces students to the axiomatic set theory of John von Neumann, Paul Bernays, and Kurt Gödel (known as NBG). Topics include union, intersection, complement, difference, power class, manifold union and intersection, axiom of unions, axiom of pairing, axiom of subsets, the empty class, the universal class and the Russell class, Russell's Paradox, successor of a class, inductive class, axiom of infinity, axiom of regularity, the whole numbers, mathematical induction, and the well-ordering principle.

Description:
This honors course introduces students to the concepts of relations, mappings, and functions. Topics include ordered pairs; relations and their converses; domain, range and field of a relation; reflexivity, symmetry, transitivity, asymmetry, antisymmetry, connectivity of relations; functions as special relations; mappings as targeted functions; injective and surjective mappings; and equivalence relations, equivalence classes.