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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

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FS Hallmarks and Explanatory Notes

(Foundations Board approved 09/19/06; modified by the Foundations Multicampus Group on 05/02/12)

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. include computational and/or quantitative skills. [modified 5/2/12]
    • The course will not focus solely on computational skills, i.e., the application of algorithmic processes leading to determinant answers. [added 5/2/12]

    • 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, FS-FQ and FQ Courses at UHM

Effective Fall 2018, Quantitative Reasoning (FQ) replaces Symbolic Reasoning (FS) as a General Education requirement.

To ensure there is adequate time for students who entered the UH System prior to Fall 2018 to complete their FS requirements, FS-FQ courses will be offered through Summer 2023 at UH Mānoa. FS and FS-FQ courses will be offered through Summer 2020 at UH community colleges.

Students should contact their designated School/College academic or faculty advisor for more information.

FS Courses

  • ICS 241*, Discrete Mathematics for Computer Science II F02-SS18
  • PHIL 110, Introduction to Deductive Logic F02-SS18
  • PHIL 110A, Introduction to Deductive Logic Honors F02-SS18

FS-FQ Courses

  • BUS 250, Applied Math in Business F18-SS23 (FS F03-SS18)
  • ICS 141, Discrete Mathematics for Computer Science I F18-SS23 (FS F02-SS18)
  • MATH 100, Survey of Mathematics F18-SS23 (FS F02-SS18)
  • MATH 112*, Math for Elementary Teachers II F18-SS23 (FS F05-SS18)
  • MATH 140**, Precalculus: Trigonometry and Analytic Geometry F18-SS23 (FS F02-SS18)
  • MATH 161, Precalculus and Elements of Calculus for Economics and the Social Sciences F18-SS23 (FS SS11-SS18)
  • MATH 203**, Calculus for Business and Social Sciences F18-SS23 (FS F02-SS18)
  • MATH 215**, Applied Calculus I F18-SS23 (FS F02-SS18)
  • MATH 241**, Calculus I F18-SS23 (FS F02-SS18)
  • MATH 251A**, Accelerated Calculus I F18-SS23 (FS F02-SS18)
  • NREM 203, Applied Calculus for Management, Life Sciences, and Human Resources F18-SS23 (FS F03-SS18)

FQ Courses

  • ANTH 220, Quantitative Reasoning for Anthropologists F18-SS21
  • ATMO/GG/OCN 150, Introduction to Quantitative Earth and Environmental Science F18-SS21
  • GG 102, Quantifying Global and Environmental Change F18-SS21
  • PH 210, Quantitative Reasoning for Public Health F18-SS21
  • PHIL 111, Introduction to Inductive Logic F18-SS23 (FS F03-SS18)

* Has a prerequisite.
** Requires placement by the
Math Department's Precalculus Assessment.

FS Courses no longer offered at UHM

  • ECON 301, Intermediate Microeconomics F03-S08
  • MATH 100A, Survey of Mathematics Honors F02-SS12
  • MATH 111, Math for Elementary Teachers I F03-SS05
  • MATH 215A, Applied Calculus I Honors F02-SS12
  • MATH 241A, Calculus I Honors F02-SS12
  • MATH 251, Accelerated Calculus F02-SS07
  • SOCS 150, Street Science: Evaluating and Applying Evidence in Daily Life F11-SS14

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last updated December 18, 2017; report errors to gened@hawaii.edu