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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
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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)
  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

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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

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last updated June 7, 2012; report errors to gened@hawaii.edu