Analyzing Mathematcal Paterns —

Detecton & Formulaton

Inductve Approach to Recogniton, Analysis and Formulatons of Paterns

Michael A Radin Rochester Insttute of Technology, USA

Key Features

• he book provides several repettve t pe guided e amples that navigate to deeper undamentals and to solving more challenging problems

• hese practce problems lead to ormulatng pa erns, to inductve reasoning and to proo b inducton

• he book introduces the inductve approach to grasp the concepts

• he book presents each concept graphicall and anal tcall and the connecton between the two methods

• he book also emphasi es the similarites and contrasts between assorted pa erns and widens the readers anal tcal skills and welcomes them to un old more mathematcal essences

Descripton

The book’s objectves are to expose students to analyzing and formulatng various paterns such as linear, quadratc, geometric, piecewise, alternatng, summatontype, product-type, recursive and periodic paterns. he book will present various pa erns graphicall and anal tcall and show the connectons between them. Graphical presentatons include pa erns at same scale, pa erns at diminishing scale and alternatng pa erns.

he book s goals are to train and e pand students anal tcal skills b presentng numerous repettve t pe problems that will lead to ormulatng results inductvel and to the proo b inducton method. hese will start with ormulatng basic se uences and piecewise unctons and transiton to propertes o Pascal s riangle that are hori ontall and diagonall oriented and ormulatng solutons to recursive se uences. he book will start with relatvel straight orward problems and graduall transiton to more challenging problems and open ended research uestons.

he book s aims are to prepare students to establish a base o recogniton and ormulaton o pa erns that will navigate to stud urther mathematcs such as Calculus, iscrete athematcs, atri lgebra, bstract lgebra, i erence E uatons, and to potental research pro ects. he primar aims out o all are to make mathematcs accessible and multdisciplinar or students with di erent backgrounds and rom various disciplines.

Author

Michael A Radin earned his Ph at the Universit o hode sland in 200 and is currentl an associate pro essor o mathematcs at the ochester nsttute o echnolog . ichael started his ourne anal ing di erence e uatons that portra periodic and eventuall periodic c cles as part o his Ph thesis. He has several publicatons on the boundedness and periodic nature o solutons o ratonal di erence e uatons, ma t pe di erence e uatons and piecewise di erence e uatons. uring the last 20 ears, ichael published several papers together with his undergraduate and graduate students at and has publicatons with students and colleagues rom iga echnical Universit , Universit o Latvia, Pskov State Universit and aroslavl State Universit .

January 2023

£80 | HARDCOVER 978 98 26 04 6

£45 | SOFTCOVER 978 98 26 2 0 4

Imprint: World Scientfc Publishing Compan

Extent: 290pp

Type: e tbook

Main Subject: athematcs

Sub-Subjects: athematcs Educaton Combinatorics i erence nd unctonal E uatons General pplied athematcs General Pure athematcs eaching nd Learning

Keywords: Pa ern ecogniton nducton Geometrical Confguratons Pa erns at Same Scale Pa erns at i erent Scales lternatons Pa erns Piecewise Pa erns ecursive Pa erns Periodic Pa erns

Readership: High school and undergraduate levels in mathematcs or on S E disciplines, Pa ern ecogniton, iscrete athematcs, i erence E uatons

• Introducton to Paterns:

Geometrical Confguratons

Piecewise Functons

Analytcal Formulatons

Recursive Sequences

Piecewise Sequences

Periodic Cycles

• Geometrical Confguratons:

Paterns at Same Scale

Paterns at Diferent Scales

Alternatng & Piecewise Paterns

Summaton of Areas

Sequences, Products & Summatons:

Linear Sequences

Quadratc Sequences

Summaton–Type Sequences

Geometric Sequences

Product–Type Sequences

Alternatng & Piecewise Sequences

• Summatons & Proof by Inducton:

3Linear & Geometric Summatons

Proof by Inducton

Traits of Pascal’s Triangle:

Horizontal Identtes

Diagonal Identtes

Binomial Expansion

• Recursive Relatons:

Formulatng a Recursive Relaton

Obtaining an Explicit Soluton

Non-autonomous Recursive Sequences

• Periodic Traits: utonomous ecursive Se uences ultplicatve orm dditve orm ultplicatve dditve orms