

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; 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)
 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.
 nontrivial
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.
 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.
 build a bridge from theory to
practice and show students how to traverse this bridge.
 Students should be
able to abstract from a realworld 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, FSFQ 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, FSFQ courses will be offered through Summer 2023 at UH Mānoa. FS and FSFQ 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 F02SS18
 PHIL 110, Introduction to Deductive Logic F02SS18
 PHIL 110A, Introduction to Deductive Logic Honors F02SS18
FSFQ Courses
 BUS 250, Applied Math in Business F18SS23 (FS F03SS18)
 ICS 141, Discrete Mathematics for Computer Science I F18SS23 (FS F02SS18)
 MATH 100, Survey of Mathematics F18SS23 (FS F02SS18)
 MATH 112*, Math for Elementary Teachers II F18SS23 (FS F05SS18)
 MATH 140**, Precalculus: Trigonometry and Analytic Geometry F18SS23 (FS F02SS18)
 MATH 161, Precalculus and Elements of Calculus for Economics and the Social Sciences F18SS23 (FS SS11SS18)
 MATH 203**, Calculus for Business and Social Sciences F18SS23 (FS F02SS18)
 MATH 215**, Applied Calculus I F18SS23 (FS F02SS18)
 MATH 241**, Calculus I F18SS23 (FS F02SS18)
 MATH 251A**, Accelerated Calculus I F18SS23 (FS F02SS18)
 NREM 203, Applied Calculus for Management, Life Sciences, and Human Resources F18SS23 (FS F03SS18)
FQ Courses
 ANTH 220, Quantitative Reasoning for Anthropologists F18SS21
 ATMO/GG/OCN 150, Introduction to Quantitative Earth and Environmental Science F18SS21
 GG 102, Quantifying Global and Environmental Change F18SS21
 PH 210, Quantitative Reasoning for Public Health F18SS21
 PHIL 111, Introduction to Inductive Logic F18SS23 (FS F03SS18)
* Has a prerequisite.
** Requires placement by the
Math Department's Precalculus Assessment.
FS Courses no longer offered at UHM
 ECON 301, Intermediate Microeconomics F03S08
 MATH 100A, Survey of Mathematics Honors F02SS12
 MATH 111, Math for Elementary Teachers I F03SS05
 MATH 215A, Applied Calculus I Honors F02SS12
 MATH 241A, Calculus I Honors F02SS12
 MATH 251, Accelerated Calculus F02SS07
 SOCS 150, Street Science: Evaluating and Applying Evidence in Daily Life F11SS14
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last updated December
18, 2017; report errors to gened@hawaii.edu 