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Foundations - Symbolic Reasoning (FS)
Courses fulfilling this requirement will expose students to the beauty and power of formal systems, as well as to their
clarity and precision; courses will not focus solely on computational skills. Students should understand the concept
of proof as a chain of inferences. They should be able to apply formal rules or algorithms. They should also be able
to engage in hypothetical reasoning. In addition, the course should aim to develop the ability of students to use
appropriate symbolic techniques in the context of problem solving, and in the presentation and critical evaluation of
evidence.
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FS Hallmarks and Explanatory Notes
FS courses
Related links:
Foundations articulation
Foundations assessment
FS Hallmarks and Explanatory Notes
(Foundations
Board approved 09/19/06)
To satisfy the Symbolic Reasoning (FS) requirement, a course
will (Hallmarks in
bold; Notes in italics)
- expose students to the beauty,
power, clarity and precision of formal systems.
- Students should
understand the impact of formal or symbolic reasoning in its application
to other disciplines and/or its historical place in civilization.
- An objective of the FS
requirement is to enhance students’ appreciation of abstraction and
formal systems of analysis and to elevate their power of critical
thinking through logical analysis and use of evidence.
- Students may be
exposed to the power, clarity and precision of formal systems by reading
and understanding proofs, derivations of formulae, or expositions of
applications. Students may also be exposed to the power, clarity and
precision of formal systems by constructing proofs (including symbolic
proofs of validity), deriving formulas of appreciable applicability, or
justifying the uses of applications in concrete context. In any of these
situations, formal reasoning and/or symbolism should play a significant
or essential role.
- The exposure to the
beauty of formal systems can be provided by the presentation of elegant
proofs, tricky, i.e., creative, applications of formulae, or the
derivation of unexpected applications.
- help students understand the
concept of proof as a chain of inferences.
- non-trivial
component of the course should be deductive proof.
- Students should be
required to demonstrate an understanding of the difference between a
correct and incorrect proof.
- Students should
understand the distinction between inductive and deductive, formal and
informal reasoning.
- Students should be
familiar with all aspects of basic argumentation: (1) the recognition of
premises, given statements or hypothesis, (2) the recognition of the
conclusion as well as noticing that a proof has appropriately come to an
end since the conclusion has been justified, (3) the recognition of the
application of the principles of logic to the premises, earlier steps or
recognized truths to justify subsequent steps.
- Students should be
able to construct formal arguments and be expected to justify most steps
of an argument.
- teach students how to apply
formal rules or algorithms.
- Students should be
able to correctly apply rules of a formal system.
- Students should be
introduced to a process of applying formal rules, so that students will
understand the importance of paying attention to detail and why
precision is crucial, and how rule generation works in carrying out
mechanical, logical, and/or computational procedures.
- require students to use
appropriate symbolic techniques in the context of problem solving, and
in the presentation and critical evaluation of evidence.
- Students should be
able to recognize the elements, structure and standards of rigorous
arguments and distinguish between correct and incorrect argument.
- Students should be
able to recognize appropriate and inappropriate use of words and
symbolism, statements as opposed to meaningless sentences, valid and
invalid arguments, as well as valid and invalid applications of symbolic
reasoning.
- not focus solely on
computational skills.
- Students should be
challenged to use symbolic trails of reasoning not only minimally but in
maximally efficient and elegant ways.
- Students should not be
simply trained in mechanical, computational or formulaic techniques.
- build a bridge from theory to
practice and show students how to traverse this bridge.
- Students should be
able to abstract from a real-world situation to formal, symbolic
representation.
- Students should be
able to translate word problems or arguments into an appropriate
symbolic formalism.
- Students should see
the development of a “useful” application from a theoretical or formal
idea. In that development it should be made especially clear that the
use of symbolism facilitated the exposition that lead from theory to
practice.
- Students will learn
that arguments and procedures expressed in ordinary language can be
checked with great precision by placing the reasoning patterns in
symbolic form and manipulated via symbolic rules of inference.
TOP
Approved FS Courses at UHM
Effective term=Fall 2002 unless otherwise noted
- Business 250* [effective F03-]
Economics 301 [FS effective F03-S08]- Information Computer Science 141
- Information Computer Science 241*
- Math 100
Math 100A [no
longer offered]Math 111 [effective F03-SS05]- Math 112* [effective F05-]
- Math 140**
- Math 161 [effective SS11-]
- Math 203**
- Math 215**
Math 215A [no
longer offered]- Math 241**
Math 241A [no longer
offered]Math 251 [no
longer offered]- Math 251A**
- Natural Resources & Environmental Management 203 [effective F03-]
- Philosophy 110
- Philosophy 110A
- Philosophy 111 [effective F03-]
- Social Sciences 150 [effective
F11-SS14]
* Has a prerequisite.
** Requires placement by the
Math Department's Precalculus Assessment.
"A" courses are offered by the
Selected Studies/Honors Program
TOP
last updated June 7, 2012; report errors to gened@hawaii.edu |
