Kuldeep Singh

Number theory is one of the oldest branches of mathematics that is primarily concerned with positive integers. While it has long been studied for its beauty and elegance as a branch of pure mathematics, it has seen a resurgence in recent years with the advent of the digital world for its modern applications in both computer science and cryptography. Number Theory: Step by Step is an undergraduate-level introduction to number theory that assumes no prior knowledge, but works to gradually increase the reader's confidence and ability to tackle more difficult material. The strength of the text is in its large number of examples and the step-by-step explanation of each topic as it is introduced to help aid understanding the abstract mathematics of number theory. It is compiled in such a way that allows self-study, with explicit solutions to all the set of problems freely available online via the companion website. Punctuating the text are short and engaging historical profiles that add context for the topics covered and provide a dynamic background for the subject matter.

This special 20th anniversary anthology invites you to journey outside yourself: float in a capsized rowboat, downward-dog through a yoga studio adapting to covid-19, reflect on the legacy of residential schools, find purpose on the Camino de Santiago, and make peace with your raccoon neighbours. These are stories of ego, loss, birth, renewal-the salient issues of our time. In emerge 20, stories in fiction, narrative non-fiction, speculative fiction, young adult fiction, poetry, and lyric prose isolate the everyday tales of human resilience and solidarity that will leave you wanting more from these emerging writers. CONTENTSBetsy Warland-ForewordFICTIONDora Joella Prieto-The Last Wisdom ToothElliott Gish-Grey DogB. B. Randhawa-The Woman Who Thought She Was a CowTeminey Beckers-My Name Is BadgerDora Larson-The ApartmentPrachi Kamble-World Class EducationBarbara Cameron-Unconsecrated GroundAngela Kruger-Hotel Blue: StoriesFrederic Sahyouni-The Fragrant HarbourColleen Doty-All About IsaacLibby Soper-The Anniversary Cakeeve nixen-Two storiesSarah Phillips-Thin-Grasping at the PineappleFrancesca Mauri -The Day of Her DisappearanceAnya Wyers-Romilegal: DowntownUttara Krishnadas-InfectiousJudy Dercksen-Not the Namib DesertMagnus Lu-Ten Days of UndoingStephanie Peters-The UpsetDK Eve-Lunch Shift at the Castle Caf Tanya Belanger-The Last StopVisnja Milidragovic-Happy HourRebecca Chan-An Unnatural WidowHugh Griffith-The Snake ClubSandra Sugimoto-SistersChristina Kruger-Woodrow-Lie FallowNON-FICTIONKatie Lewis-NutsWilliam W. Campbell-Amusia and Ravel's Bol roKim Spencer-Two piecesLori Greenfield-The Tuesday LadiesEmily Chan-Living in Ms. Shauna Roberts's ApartmentJustyna Krol-System FailureEmma Brady-The BedroomNancy Jin-GuifangDeborah Folka-Dessert in the DesertShenul Dhalla-Hope for a CureChristine Pilgim-GoodbyeMaryanna Gabriel-Get Thee to a NunneryOla Szczecinska-Big SurCalvin McShane-Catching the Way ZendoMargaret Miller-Two piecesAnne Rosenberg-Two piecesKate Covello-Disruption and Innovation: Yoga Teacher Training After covid-19Ankush Chopra-Stay the CourseSPECULATIVE AND YA FICTIONJenn Marx-Electric Blue TongueJess Wesley-The Curse of the Fairy QueenHannah Costelle-The Dressmaker of DrumchapelDiane Dubas-EnoughClare McNamee-Annett-We Are Doing FineLibby McKeever-What Came BeforeKatherine Fawcett-Ursula MediumSky Regina-We Are ApricotsTim J. O'Connor-Kath's PartyErin Pettit-Gilded CityElizabeth Page-Price of PrivilegeDaniel Ortiz Rubio-Purple StainSofia Pezentte-The Blameless OneStephanie Charette-To Hunt the MountainL a Taranto-Kiss the GroundSusan Taite-GlimmersJack Murphy-Hyper Neon CowboyBailey Bjolin-DomeDanica Longair-Hope Is a Necessary DelusionRobert Weber-The End Is ... Mundane? POETRYAlana Cheyne-Three poemsEla Przybylo-Two poemsAnna Lee-Popham-Three poemsBrandon Houston-Can I Pray for YouKuldeep Singh-Five poemsPinki Li-To the Family of Raccoons Who Moved in Late Last WeekSarah Jessie Tucker-Four poemsF. J. Erica Yang-The Frightfully Pale YellowLaura McGavin-Two poemsClare Adam-Two poemsAmrit Kaur Sanghera-Moving Another WayMarco Melfi-A Model From Bosch's The Garden of Earthly Delights ReminiscesMichael Edwards-Two poemsTharuna Abbu-Three poems

This book is a practical guide to latest procedures and diagnostic guidelines for use of sonography in gynaecology. Beginning with an introduction to the role of ultrasound and patient preparation, the following chapters cover common pathologies, uterocervical abnormalities, colour flow mapping, and duplex Doppler. All the latest advances have been included to ensure clinicians are fully up to date in their field. The book features nearly 500 2D, 3D and 4D ultrasound images, with a corresponding image for most of the pathologies described in the text. Key Points Practical guide to latest procedures and diagnostic guidelines for gynaecologic sonographyProvides overview of role of ultrasound and patient preparationCovers common pathologies, abnormalities, and different types of ultrasoundIncludes nearly 500 2D, 3D and 4D ultrasound images

Monitoring the heart beat of a foetus is especially difficult due to constant changes in foetal position. This book is an easy to use reference providing physicians and sonographers with useful tips on how best to perform a foetal echocardiograph, allowing them to accurately evaluate normal and abnormal heart beat. Basic cardiac anatomy is described in detail and numerous ultrasound images assist understanding. Key points Concise guide to performing a foetal echocardiographAllows easy comparison of normal and abnormal heart beatBasic cardiac anatomy described in detailIncludes nearly 200 ultrasound images

Linear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance. The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader's confidence. Also included, generally at the beginning of sections, are short historical biographies of the leading players in the field of linear algebra to provide context for the topics covered. The dynamic and engaging style of the book includes frequent question and answer sections to test the reader's understanding of the methods introduced, rather than requiring rote learning. When first encountered, the subject can appear abstract and students will sometimes struggle to see its relevance; to counter this, the book also contains interviews with key people who use linear algebra in practice, in both professional and academic life. It will appeal to undergraduate students in mathematics, the physical sciences and engineering.

3D ultrasound shows a still image of a foetus, far more detailed than the 2D flat grey scale imaging. 4D ultrasound is more advanced, showing a moving image, allowing obstetricians to evaluate foetal well-being. It is also used by gynaecologists to examine uterine anomalies. The second edition of this book is a step by step guide to 3D and 4D ultrasound in obstetrics, gynaecology and infertility. Divided into seven sections, it begins with discussion on instruments and scanning techniques, and normal pelvic anatomy by ultrasound. The following chapters examine uterine lesions and the use of ultrasound for infertility evaluation. The final sections discuss 3D/4D ultrasound in early pregnancy and foetal anatomy and malformations in mid and late pregnancy. This concise handbook has been fully updated to include the latest developments in 3D/4D ultrasound, and includes nearly 220 detailed photographs and ultrasound images. Key points Fully updated, new edition presenting latest developments in 3D and 4D ultrasound in obstetrics, gynaecology and infertilityDescribes normal pelvic anatomy to help recognition of anomalies and malformationsIncludes numerous clinical photographs and ultrasound imagesPrevious edition published in 2008

This popular, world-wide selling textbook teaches engineering mathematics in a step-by-step fashion and uniquely through engineering examples and exercises which apply the techniques right from their introduction. This contextual use of mathematics is highly motivating, as with every topic and each new page students see the importance and relevance of mathematics in engineering. The examples are taken from mechanics, aerodynamics, electronics, engineering, fluid dynamics and other areas. While being general and accessible for all students, they also highlight how mathematics works in any individual’s engineering discipline. The material is often praised for its careful pace, and the author pauses to ask questions to keep students reflecting. Proof of mathematical results is kept to a minimum. Instead the book develops learning by investigating results, observing patterns, visualizing graphs and answering questions using technology. This textbook is ideal for first year undergraduates and those on pre-degree courses in Engineering (all disciplines) and Science. New to this Edition:- Fully revised and improved on the basis of student feedback- New sections- More examples, more exam questions- Vignettes and photos of key mathematiciansAccompanying online resources for this title can be found at bloomsburyonlineresources.com/engineering-mathematics-through-applications-2. These resources are designed to support teaching and learning when using this textbook and are available at no extra cost.

Engineering Mathematics through Applications is a new reference and self-study guide for professionals and students which uses applications from a wide range of technical disciplines to help teach the subject and convey its relevance. The mathematics is developed through clear and easy step-by-step examples rather than formal proofs, and the mathematical theory is supported by the use of technology in solving real life engineering problems. The answers to all the questions are included within, while complete worked solutions are available on the accompanying website. Provides complete detailed solutions to carefully selected exercises that reinforce the text, making it ideal an ideal self-study guide. Written in a chatty, user-friendly manner that will help motivate the reader. For those who might need it, an optional introductory refresher chapter covering indices, fractions, decimals, percentages and ratios is offered. Contains calculator and mathematical software examples and exercises. Arithematic for EngineersEngineering FormulaeVisualizing Engineering FormulaeFunctions in EngineeringTrigonometry and WaveformsLogarithmic, Exponential and Hyperbolic FunctionsDifferentiationEngineering Applications of DifferentiationIntegrationEngineering Applications of IntegrationComplex NumbersMatricesVectorsFirst Order Differential EquationsSecond Order Linear Differential EquationsPartial DifferentiationProbability and StatisticsSolutionsAppendix: Standard Normal Distribution TableIndex