Computational Thinking: A Perspective on Computer Science

338 Pages·2021·9.019 MB·English

by  Zhiwei Xu, Jialin Zhang

Zhiwei Xu · Jialin Zhang
Computational
Thinking:
A Perspective on
Computer Science
Computational Thinking: A Perspective on
Computer Science
(cid:129)
Zhiwei Xu Jialin Zhang
Computational Thinking:
A Perspective on Computer
Science
ZhiweiXu JialinZhang
UniversityofChineseAcademy UniversityofChineseAcademy
ofSciences ofSciences
Beijing,China Beijing,China
ISBN978-981-16-3847-3 ISBN978-981-16-3848-0 (eBook)
https://doi.org/10.1007/978-981-16-3848-0
©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSingapore
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To Hao, for continuous inspiration and
support
Zhiwei
To my husband and little son, with love
Jialin
Preface
This book provides an introduction to computer science from the computational
thinking perspective. It explains the way of thinking in computer science through
chapters of logic thinking, algorithmic thinking, systems thinking, and network
thinking.Itispurposelydesignedasatextbookforthefirstcomputersciencecourse
servingundergraduatesfromalldisciplines.
Thebookfocusesonelementaryknowledgesuchthatallmaterialcanbecovered
inaone-semestercourseofIntroductiontoComputerScience.Itisdesignedforall
students, assuming no prior programming experience. At the same time, students
withpriorprogrammingexperienceshouldnotfindthecourseboring.
Thebookpracticesanactivelearningmethod,utilizingrecentadvicebyDonald
Knuth:“TheultimatetestofwhetherIunderstandsomethingisifIcanexplainittoa
computer.”Thebookisdesignedtoenablestudentstorisefromthebasementlevel
of remembering to the top level of creating in Bloom’s taxonomy of education
objectives.Morethan200hands-onexercises,thoughtexperiments,andprojectsare
includedtoencouragestudentstocreate.Examplesofcreativetasksinclude:
(cid:129) DesignaTuringmachinetodon-bitaddition,wherencouldbearbitrarilylarge.
Thiscouldbeastudent’sfirstdesignofanabstractcomputer.
(cid:129) Designateamcomputertodoquicksort.Thiscouldbeastudent’sfirstdesignofa
realcomputer,includingitsinstructionsetandmachineorganization.
(cid:129) Develop a computer application (a steganography computer program) to hide a
textfilehamlet.txtinapicturefileAutumn.bmp.
(cid:129) Design a smart algorithm and a program to compute Fibonacci numbers F(n),
wherencouldbeaslargeasonemillionorevenonebillion.
(cid:129) Create a dynamic webpage of creative expression for a Kitty Band, which can
playapieceofmusicgivenaninputstringofmusicscores.
ThematerialofthebookhasbeenusedintheUniversityofChineseAcademyof
Sciencessince2014,servingarequiredcourseforfreshmenfromallschools.Itwas
vii
viii Preface
also used in summer schools organized by China Computer Federation, to train
universityandhigh-schoolinstructorsonteachingaComputerFundamentalscourse
utilizingcomputationalthinking.
Supplementarymaterialisprovidedatcs101.ucas.edu.cn.
Beijing,China ZhiweiXu
October2021 JialinZhang
Introduction
Thistextbookisforaone-semestercourseofIntroductiontoComputerScience(e.g.,
CS101),targetingundergraduatestudentsfromalldisciplines.Itisaself-contained
book with no prerequisites. The little prior knowledge and notations needed are
explainedalongthewayandsummarizedinAppendices.
The book is designed to introduce elementary knowledge of computer science
andthefield’swayofthinking.Ithasthefollowingfourobjectivesandfeatures:
(cid:129) Embodyingcomputationalthinking.Thewayofthinkingincomputerscienceis
characterized by three features without and eight understandings within. Intro-
ductory bodies of knowledge are organized into chapters of logic thinking,
algorithmicthinking,systemsthinking,andnetworkthinking.
(cid:129) AimingatupperlevelsofBloom’staxonomy,withasignificantportionoflearning
material going from “remember” to “create,” as shown in Fig. 1. The learning
methodusesKnuth’sTest:“TheultimatetestofwhetherIunderstandsomething
is if I can explain it to a computer.” More than 200 hands-on exercises and
thoughtexperimentsareincludedtoencouragestudentstocreate.
(cid:129) Focusing on elementary knowledge without dumbing down. An explicit goal is
that all material should be coverablein one semester, for a class of hundreds of
students of all disciplines, assuming no prior programming experiences. At the
sametime,experiencedstudentsshouldnotfindthecourseboring.
(cid:129) Learning froma decade ofeducational experience. We spent 4 years designing
the course and 6 years teaching the material. The contents have gone through
three major revisions. For instance, version 1 has no programming. Version
2 includes Go language programming contents. Version 3 (the current version)
requires a student to write roughly 300 lines of Go code and 100 lines of Web
code,wheremoststudentscanlearnWebprogrammingbythemselves.
ix
x Introduction
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Bloom’s Taxonom Produce new or original workDesign, assemble, consturct, conjecture, develop, formulate, author, investigate Justify a stand or decisionappraise, argue, defend, judge, select, support, value, critique, weigh Draw connections among ideasdifferentiate, organize, relate, compare, contrast, distinguish, examine,experiment, question, test Use information in new situationsexecute, implement, solve, use, demonstrate, interpret, operate,schedule, sketch Explain ideas or conceptsclassify, describe, discuss, explain, identify, locate, recognireport, select, translate Recall facts and basic conceptsdefine, duplicate, list, memorize, repeat, state Vanderbilt University Center for Teaching ’eshowingBloomstaxonomybyVandyCFTislicensedunderCCBY2.0)
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Introduction xi
Problem-Solving Examples
Computerscienceisasubjectstudyingcomputationalprocessesinproblem-solving
and creative expression. This textbook includes over 200 problems as examples,
exercises, and hands-on projects. They provide a glimpse of how computers work
andwhatkindsofproblem-solvingandcreativeexpressionareenabledbycomputer
scienceandcomputationalthinking.
Thebookshowshowtosolvesuchproblems.Indoingso,itintroduceselemen-
tary knowledge on not only how to use a computer but also how to design a
computer. We demonstrate that computer science is intellectually interesting, by
heeding Donald Knuth’s advice: “In most of life, you can bluff, but not with
computers.”Wetakespecialcaretoavoidunderestimatingthepotentialsofstudents
anddumbingdownthecoursematerial.
SixrepresentativeproblemsareshownbelowandillustratedinFig.2.
(cid:129) DesignaTuringmachinetodon-bitaddition,wherencouldbearbitrarilylarge,
such as n ¼ 23 ¼ 8, n ¼ 210 ¼ 1024, or n ¼ 220 ¼ 1048576. This could be a
student’sfirstabstractcomputer.
(cid:129) Design a human-computer to do quicksort. A student is asked to design a team
computer to successfully rearrange a group of students ordered by students’
names to another group ordered by students’ heights, as shown in Fig. 2a. This
could be a student’s first design of a working real computer, complete with its
instructionsetandmachineorganizationofessentialcomponents.
(cid:129) Compute the area of a panda. Computer science offers new abilities to solve
problems beyondordinary school math, suchas computing theirregular area of
the panda picture in Fig. 2b. The same computer application idea extends to
irregular shapes ofmultiple dimensions,and “area”can be replaced byvolume,
mass,energy,numberofparticles,etc.
(cid:129) ComputeFibonaccinumbersF(n),wherencouldbeaslargeasonebillion.This
problem reveals how smart algorithms, together with systems support, can
drasticallyreducecomputingtime,from2ntonorevenlogn.
(cid:129) Prove a problem belonging to P or NP, intuitively. Students are asked to prove
whetherasimpleproblembelongstoPorNP.Forsuchalgorithmiccomplexity
materialtobeincludedinanintroductorycourse,theproblemandtheproofmust
beintuitivelysimple,involvingonlyelementarymathematicsandashortreason-
ing sequence. A sample problem is the following: decide if 2n numbers can be
divided into two groups, each having n numbers, such that the sums of the two
groupsareequal.
(cid:129) CreateKittyBand.Studentsareaskedtocreateadynamicwebpageshowingtheir
personalartifacts.AnexampleisprovidedbyMissSiyueLioftheUniversityof
Chinese Academy of Sciences, who created the Kitty Band work of creative
expression,asshowninFig.2c.Thiswittybandcanplayapieceofmusicgiven
aninputstringofmusicscores.AsafreshmanofPhysicsmajor,shefinishedthis
projectin3days.Halfofhertimewasspentonthinking,designing,andmaking.
Codinganddebuggingaccountedfornomorethan50%ofthetime.