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Zinn & the Art of Road Bike Maintenance: The World's Best-Selling Bicycle Repair and Maintenance Guide, 6th Edition
by Lennard ZinnJoin the millions of cyclists who swear by the name Zinn. Now in its sixth edition, Zinn & the Art of Road Bike Maintenance is the world&’s best-selling guide to bicycle repair and maintenance. Lennard Zinn is the world&’s leading expert on bike maintenance and repair. From basic repairs like how to fix a flat tire to advanced overhauls of drivetrains and brakes, his illustrated, step-by-step guide explains the tools you&’ll need and how to know you&’ve done the job right. This book's interior is easy to read, even in a dimly lit garage or workshop. Hundreds of hand-drawn illustrations and exploded parts diagrams show just the right level of detail to lead you through every bicycle repair task. In over 450 pages, Zinn&’s guide includes simple instructions for hundreds of bike maintenance and repair jobs, including: Basics: How to fix a flat tire, lube a bicycle chain, adjust the brakes Emergency repairs: How to fix a broken chain, tighten loose spokes, repair a bent derailleur Easy shifting: How to adjust shifters, derailleurs, and cables for clean and smooth shifting Wheels: How to true a wheel, install a new tire, change a cassette, replace broken spokes, build your own wheels Overhauls: How to service and replace pedals, chains and chainrings, saddles, handlebars, stems, headsets, forks, bottom brackets New tech: How to maintain 11-speed systems, electronic and wireless shifters, disc brakes Cyclocross: How to set up a &’cross bike for racing, select the right components, and make quick repairs Troubleshooting: How to figure out what&’s wrong with any bike and fix it This sixth edition of Zinn & the Art of Road Bike Maintenance also includes more than 50 new illustrations as well as completely new information on routing internal wires, cables, hoses, and housing; how to pack bikes for shipping and air travel; repair on the road tips for tubeless tires; how to chain wax, and so much more. This guide makes bicycle repair and maintenance easy, quick, affordable, and fun. With Zinn at your side, you&’ll know how to keep your bicycling running smoothly for years.
Defying "The Plan": Intimate Politics among Palestinian Women in Israel
by Kim Jezabel ZinngrebeLiving under settler colonialism and patriarchal oppressions, Palestinian women in Israel are expected to operate even the most intimate aspects of their lives according to what some call "The Plan," which dictates everything from clothing, marriage, religion, and sex to how children are born and raised. In Defying "The Plan," Kim Jezabel Zinngrebe draws from a series of moving interviews to reveal that despite various forms of intertwined oppressions by both the Israeli state and Palestinian society, Palestinian women show defiance by the quotidian choices they make in their own intimate lives under occupation, which, Zinngrebe argues, cannot be perceived as a mere corollary but constitute a pivotal and contested terrain of the struggle between settler and colonized. Defying "The Plan" explores such issues as the segregation of sexual education in Palestine; the politics of dress, menstruation, and tattoos; and the roles of class, feminism, and race. Importantly, she highlights the intersectional experiences of women typically excluded from existing accounts, such as Black Palestinian women, women with disabilities, unmarried and divorced women, Bedouin women, and LGBTQI women. The stories gathered in Defying "The Plan" trace and unpack settler colonial power at the level of the intimate and native women's various practices of defiance.
A Sociological Approach to Commodification: The Case of Transforming the Post-Socialist Society in Poland (Routledge Advances in Sociology)
by Marek Ziółkowski Rafał Drozdowski Mariusz BaranowskiThis book analyses the processes of commodification and decommodification which have wrought changes in Polish society since 1945. Examining the case of Poland, this book also explores comparisons to other countries in the Eastern European region. It is the first book to capture long-term social change from the perspective of commodification and decommodification processes. This book will appeal to sociologists, economists, historians, anthropologists and political scientists, especially to students and scholars interested in theoretical economics and economic sociology as well as Central and Eastern Europe.
Natalia Ginzburg's Global Legacies (Italian and Italian American Studies)
by Saskia Elizabeth Ziolkowski Stiliana Milkova RoussevaOffering comparative and interdisciplinary approaches to Natalia Ginzburg, this volume situates Ginzburg’s works within major critical discourses to articulate innovative readings and mobilize further lines of inquiry. The first section, “World Literature and World Making,” uses translation practices, world literature, and transnational studies to theorize the growing popularity of Ginzburg. The second section, “Female Bodies, Voices, and Gazes,” draws on gender and queer studies, speech act theory, intersectional feminism, and media studies to begin to address gaps in Ginzburg scholarship. The last section, “Identity, Topography, and Forms,” approaches Ginzburg through the lenses of trauma studies, topography, novel and essay studies, and Jewish identity. Natalia Ginzburg’s Global Legacies both makes available in English important Italian research and builds on significant international discourses. In bridging Italian and Anglophone scholarship, the volume engages students and scholars of Comparative and Italian literature, world literature, and women’s writing, as well as general readers of Ginzburg.
The Hostess Handbook: A Modern Guide to Entertaining
by Maria ZizkaFrom the author of The Newlywed Table, this helpful handbook offers readers 100 easy entertaining recipes, party planning advice, and curated menus to pull off the most delicious and delightful of gatherings, from an epic holiday bash to a casual get-together in the backyard, or an inspired dinner party. Ready to throw a dinner party? It&’s easier than you think. With 100 crowd-pleasing recipes and expert tips and tricks, The Hostess Handbook shows how to create an event that&’s warm, joyous, and imbued with the special glowy feeling of a celebration that we never want to end. Everything you need to know is here. How to plan a fantastic menu with foolproof recipes for finger foods, make-ahead mains (because you don&’t want to be in the kitchen when your guests arrive), and festive desserts. How to get your home party-ready, whether hosting two people or twenty, with primers on setting the table, the art of serving, and flower arranging. And drinks, of course—including recipes for both classic cocktails and delicious nonalcoholic libations. Cheers!
Linear Algebra in Data Science (Compact Textbooks in Mathematics)
by Peter Zizler Roberta La HayeThis textbook explores applications of linear algebra in data science at an introductory level, showing readers how the two are deeply connected. The authors accomplish this by offering exercises that escalate in complexity, many of which incorporate MATLAB. Practice projects appear as well for students to better understand the real-world applications of the material covered in a standard linear algebra course. Some topics covered include singular value decomposition, convolution, frequency filtering, and neural networks. Linear Algebra in Data Science is suitable as a supplement to a standard linear algebra course.
The Christian Life Profile Assessment Workbook Updated Edition: Developing Your Personal Plan to Think, Act, and Be Like Jesus
by ZondervanHow can you really THINK, ACT, and BE like Jesus? Pastor Randy Frazee believes there are thirty key beliefs, practices, and virtues that help define what Jesus referred to as the two great commandments: to love God and to love others. The Christian Life Profile Assessment Workbook is designed to help you asses where you are in relationship to these beliefs, practices, and virtues. Your responses will help you answer the questions "how am I doing?" and "where do I need to grow?" After you identify areas in which you would like to grow, the workbook provides suggestions and plans to help you realize that growth, such as reading books, memorizing Scripture, attending a seminar, engaging with a mentor, or taking part in a new spiritual discipline.The Christian Life Profile journey is best experienced in a small group community that seeks to encourage, pray for, and hold each other accountable for progress. The goal is to take the profile again, one year later, to monitor the progress you make in your journey.The Christian Life Profile Assessment Workbook is also designed for use alongside the Believe product group in order to enhance the church-wide experience.
Finding Joy in All You Are: You and God, You and Others, You and Your Kids (A Mom's Ordinary Day Bible Study Series)
by ZondervanA Bible study series addressing the unique needs of moms.These 8 Bible studies help women discover God’s wisdom on how to be the best mothers, women, and disciples they can be. Each study contains 6 sessions divided into 5 flexible portions: For You Alone, For You and God’s Word, For You and Others, For You and God, and For You and Your Kids. The last section helps moms share each week’s nugget of truth with their children.• Finding Joy in All You Are helps moms discover who they are as a whole person. Everyone wants a piece of mom but this study will help a mom discover more about herself—as a mom, a believer, and a unique creation of God.
A Guide to a Better You: 20 Transformative Questions to Deepen Your Faith and Change Your Life
by ZondervanGrow in your spiritual life and live more like Jesus.A Guide to a Better You includes 20 sections, 50 prompts, and journaling space to help you better understand the Bible, become more like Jesus, and reflect on continued growth in all aspects of your life.What if you could expand your spiritual life and live more like Jesus? Have you wondered how to find ways to grow in all aspects of your faith journey as you become the best version of yourself? A Guide to a Better You is an interactive tool that will help you deepen your faith and guide you toward a more enriching spiritual life. A Guide to a Better You is organized into 20 sections, includes 50 prompts, ample space to write, and bullet journaling pages. The readings focus on questions such as:How can I develop persistence?What does and does not require forgiveness?How do I build connection between generations?How should I handle pressure?How can I take godly criticism?How can I participate in God's work? After reading, you will:identify steps to interpret the Bible.create an authentic and intentional existence in your everyday interactions and routines.make wiser decisions.recognize intentional sins and how you can do better.reflect on how you can continue to grow as a better person in your home life, career, and other areas of your life. If you are seeking a deeper relationship with God and looking for a way you can be part of God's work, A Guide to a Better You is a perfect next step. You can use this complete interactive guide independently or as part of a small group. A Guide to a Better You is also a thoughtful gift you can give to loved ones or friends for birthdays or as a holiday gift.
Rooted: The NIV Bible for Men
by ZondervanA Bible for Men That's Focused on Godly Character and Faithful Living.As the world changes around us, it can be hard to hold onto your identity as a godly man. If you are struggling to find your place as a Christian, it helps to remember that while the expectations of the world seem ever-changing, the expectations that God has for you hold true. Rooted: The NIV Bible for Men strives to help you connect with your identity in Christ as it highlights timeless virtues that are still valued today. It is designed to speak to Christian men honestly and straightforwardly about their role as Christians in the face of cultural pressures and a changing society. And it speaks to character traits men need to cultivate in today's world, like confidence rooted in inner strength, self-possessed dignity and calm, kindness, joy, and leadership based in service.Drawing on the truths of Scripture, the features in this Bible will motivate you to redeem your God-given passions, drives, and purposes so you can live out your faith. Myths articles expose commonly accepted myths of our culture that many men believe. Each article opens with the first-person story of a man who believes a particular myth and how that affects his life. Then, principles from the Bible refute the myth and offer practical guidance and help.In addition, the Think About notes take you to the heart of important topics such as money, sex, and pride. Factoid-filled Get to Know profiles introduce you to 50 men from the Bible, highlighting their strengths and weaknesses. You'll find questions to reflect on, either alone or in a small group study, in the Questions for Growth. And the Knowing God notes highlight attributes of God, teaching you that knowing the character of God can help you live as a man created in his image. Altogether, these resources offer you knowledge, wisdom, and clarity to strive to become a godly man, rooted in timeless virtues.Features:Complete text of the accurate, readable, and clear New International Version (NIV)100 Myth articles—States a commonly accepted myth that the world tells you is true, then refutes the myth with the truth of God&’s Word.50 Get to Know profiles—Interesting information about men of the Bible.200 Rooted: Questions for Growth—Questions for personal reflection or small-group study.200 Knowing God notes—Highlights an attribute of God as revealed in Scripture.300 Think About notes—short teaching notes on life topics such as money, sex, and pride.Articles to help men further their Bible study66 book introductionsSubject index
Improving Your School One Week at a Time: Building the Foundation for Professional Teaching and Learning
by Jeffrey Zoul Spiri Diamantis HowardLearn how you can work more effectively with your staff to improve your school. In this unique book, Jeffrey Zoul and Spiri Diamantis Howard reveal how a powerful tool, “Friday Focus” emails or newsletters, can help school principals communicate more proactively and consistently with their teachers while improving instruction and morale.The chapters cover 37 “Friday Focus” memos, which are organized around the school year and which cover topics such as student behavior, teacher observations, parent-teacher conferences, and more. This updated second edition offers suggestions for additional areas including artificial intelligence and equity, hope, microlearning, universal design for learning, engaging the families of ELLs, online relationship building, and gamification.Whether you’re a new or veteran school leader, these inspiring messages will help you work alongside your staff as change agents for school improvement.
Case Conceptualization and Effective Interventions: Assessing and Treating Mental, Emotional, and Behavioral Disorders (Counseling and Professional Identity)
by Lynn D. Zubernis Matthew J. SnyderWith fully integrated DSM-5 criteria and current CACREP standards, this text examines case conceptualization and effective treatments across the most common disorders encountered in counseling. The comprehensive approach helps readers develop their professional identities as well as their case conceptualization and intervention skills. Each chapter blends current theory and research with case illustrations and guided practice exercises to anchor the material in real-world application. Using an innovative new Temporal/Contextual (T/C) Model, the book provides an easy-to-apply and practical framework for developing accurate and effective case conceptualizations and treatment plans. Case Conceptualization and Effective Interventions is part of the SAGE Counseling and Professional Identity Series, which targets specific competencies identified by CACREP (Council for Accreditation of Counseling and Related Programs).
Case Conceptualization and Effective Interventions: Assessing and Treating Mental, Emotional, and Behavioral Disorders (Counseling and Professional Identity)
by Lynn D. Zubernis Matthew J. SnyderWith fully integrated DSM-5 criteria and current CACREP standards, this text examines case conceptualization and effective treatments across the most common disorders encountered in counseling. The comprehensive approach helps readers develop their professional identities as well as their case conceptualization and intervention skills. Each chapter blends current theory and research with case illustrations and guided practice exercises to anchor the material in real-world application. Using an innovative new Temporal/Contextual (T/C) Model, the book provides an easy-to-apply and practical framework for developing accurate and effective case conceptualizations and treatment plans. Case Conceptualization and Effective Interventions is part of the SAGE Counseling and Professional Identity Series, which targets specific competencies identified by CACREP (Council for Accreditation of Counseling and Related Programs).
The Only Good Priest: A Mystery (Tom & Scott Mysteries #3)
by Mark Richard ZubroFather Sebastian, the only good priest everybody knows, is dead. Pastor of a parish outside Chicago, Father Sebastian was also involved in the gay community through his work with Faith, the gay Catholic organization the diocese is trying to drive out of the church.High school teacher Tom mason, who has gained some local notoriety from his involvement in a couple of murder cases, is asked by friends to look into the priest's death; was it murder? Along with his lover Scott Carpenter, a professional baseball player, Tom plunges into ecclesiastical intrigues, the hidden underground of gay Chicago and the tragedies caused by a hypocritical church.
Surely You Can't Be Serious: The True Story of Airplane!
by David Zucker Jim Abrahams Jerry ZuckerNAMED ONE OF THE BEST COMEDY BOOKS OF 2023 AT VULTURESurely You Can't Be Serious is an in-depth and hysterical look at the making of 1980's comedy classic Airplane! by the legendary writers and directors of the hit film.Airplane! premiered on July 2nd, 1980. With a budget of $3.5 million it went on to make nearly $200 million in sales and has influenced a multitude of comedians on both sides of the camera.Surely You Can’t Be Serious is the first-ever oral history of the making of Airplane! by the creators, and of the beginnings of the ZAZ trio (Zucker, Abrahams, Zucker) – charting the rise of their comedy troupe Kentucky Fried Theater in Madison, Wisconsin all the way to premiere night. The directors explain what drew them to filmmaking and in particular, comedy. With anecdotes, behind the scenes trivia, and never-before-revealed factoids – these titans of comedy filmmaking unpack everything from how they persuaded Peter Graves to be in the movie after he thought the script was a piece of garbage, how Lorna Patterson auditioned for the stewardess role in the back seat of Jerry’s Volvo, and how Leslie Nielsen’s pranks got the entire crew into trouble, to who really wrote the jive talk. The book also features testimonials and personal anecdotes from well-known faces in the film, television, and comedy sphere – proving how influential Airplane! has been from day one.Four decades after its release, Airplane! continues to make new generations laugh. Its many one-liners and visual gags have worked their way into the mainstream culture. This fully organic expansion of the ZAZ trio’s fan-base, prompted solely by word-of-mouth, comes as no surprise to longtime fans. When all around us is in flux – laughter is priceless.
Paleofantasy: What Evolution Really Tells Us About Sex, Diet, And How We Live
by Marlene Zuk“With…evidence from recent genetic and anthropological research, [Zuk] offers a dose of paleoreality.” —Erin Wayman, Science News We evolved to eat berries rather than bagels, to live in mud huts rather than condos, to sprint barefoot rather than play football—or did we? Are our bodies and brains truly at odds with modern life? Although it may seem as though we have barely had time to shed our hunter-gatherer legacy, biologist Marlene Zuk reveals that the story is not so simple. Popular theories about how our ancestors lived—and why we should emulate them—are often based on speculation, not scientific evidence. Armed with a razor-sharp wit and brilliant, eye-opening research, Zuk takes us to the cutting edge of biology to show that evolution can work much faster than was previously realized, meaning that we are not biologically the same as our caveman ancestors. Contrary to what the glossy magazines would have us believe, we do not enjoy potato chips because they crunch just like the insects our forebears snacked on. And women don’t go into shoe-shopping frenzies because their prehistoric foremothers gathered resources for their clans. As Zuk compellingly argues, such beliefs incorrectly assume that we’re stuck—finished evolving—and have been for tens of thousands of years. She draws on fascinating evidence that examines everything from adults’ ability to drink milk to the texture of our ear wax to show that we’ve actually never stopped evolving. Our nostalgic visions of an ideal evolutionary past in which we ate, lived, and reproduced as we were “meant to” fail to recognize that we were never perfectly suited to our environment. Evolution is about change, and every organism is full of trade-offs. From debunking the caveman diet to unraveling gender stereotypes, Zuk delivers an engrossing analysis of widespread paleofantasies and the scientific evidence that undermines them, all the while broadening our understanding of our origins and what they can really tell us about our present and our future.
Sex on Six Legs: Lessons on Life, Love, and Language from the Insect World
by Marlene ZukA biologist presents a &“consistently delightful&” look at the mysteries of insect behavior (The New York Times Book Review). Insects have inspired fear, fascination, and enlightenment for centuries. They are capable of incredibly complex behavior, even with brains often the size of a poppy seed. How do they accomplish feats that look like human activity—personality, language, childcare—with completely different pathways from our own? What is going on inside the mind of those ants that march like boot-camp graduates across your kitchen floor? How does the lead ant know exactly where to take her colony, to that one bread crumb that your nightly sweep missed? Can insects be taught new skills as easily as your new puppy? Sex on Six Legs is a startling and exciting book that provides answers to these questions and many more, examining not only the bedroom lives of creepy crawlies but also some of our own long-held assumptions about learning, the nature of personality, and what our own large brains might be for. &“Smart, engaging . . . Zuk approaches her subject with such humor and enthusiasm for the intricacies of insect life, even bug-phobes will relish her account.&” —Publishers Weekly, starred review
A Different Order of Difficulty: Literature after Wittgenstein
by Karen Zumhagen-YekpléIs the point of philosophy to transmit beliefs about the world, or can it sometimes have higher ambitions? In this bold study, Karen Zumhagen-Yekplé makes a critical contribution to the “resolute” program of Wittgenstein scholarship, revealing his Tractatus Logico-Philosophicus as a complex, mock-theoretical puzzle designed to engage readers in the therapeutic self-clarification Wittgenstein saw as the true work of philosophy. Seen in this light, Wittgenstein resembles his modernist contemporaries more than might first appear. Like the literary innovators of his time, Wittgenstein believed in the productive power of difficulty, in varieties of spiritual experience, in the importance of age-old questions about life’s meaning, and in the possibility of transfigurative shifts toward the right way of seeing the world. In a series of absorbing chapters, Zumhagen-Yekplé shows how Kafka, Woolf, Joyce, and Coetzee set their readers on a path toward a new way of being. Offering a new perspective on Wittgenstein as philosophical modernist, and on the lives and afterlives of his indirect teaching, A Different Order of Difficulty is a compelling addition to studies in both literature and philosophy.
Disavowal (Theory Redux)
by Alenka ZupančičThis book argues that the psychoanalytic concept of disavowal best renders the structure underlying our contemporary social response to traumatic and disturbing events, from climate change to unsettling tectonic shifts in our social tissue. Unlike denialism and negation, disavowal functions by fully acknowledging what we disavow. Zupančič contends that disavowal, which sustains some belief by means of ardently proclaiming the knowledge of the opposite, is becoming a predominant feature of our social and political life. She also shows how the libidinal economy of disavowal is a key element of capitalist economy. The concept of fetishistic disavowal already exposes the objectified side of the mechanism of the disavowal, which follows the general formula: I know well, but all the same, the object-fetish allows me to disregard this knowledge. Zupančič adds another twist by showing how, in the prevailing structure of disavowal today, the mere act of declaring that we know becomes itself an object-fetish by which we intercept the reality of that very knowledge. This perverse deployment of knowledge deprives it of any reality.This structure of disavowal can be found not only in the more extreme and dramatic cases of conspiracy theories and re-emerging magical thinking, but even more so in the supposedly sober continuation of business as usual, combined with the call to adapt to the new reality. To disrupt this social embedding of disavowal, it is not enough to change the way we think: things need to change, and hence the way they think for us.
A Very Different War: RAAF Operations in the Korean War
by Owen ZuppThe Korean War lies between the enormity of the Second World War and the controversy of Vietnam. Although it often slips through the cracks of history, it represented a global shift as two opposing ideologies clashed and the Cold War heated up. The fledgling United Nations was called to act, and Australia joined the 21 nations committed to supporting South Korea. Within days of the North Koreans crossing the 38th Parallel, the RAAF was flying missions from its base in Japan. In the ensuing three years, the RAAF gained respect among its peers and the attention of the opposing military powers. When the war reached a crisis point, with UN forces pinned down and threatened with being pushed off the peninsula into the sea, the RAAF was at the epicentre. During the war, the RAAF entered the jet age, and the transition was not without challenges and losses. Ultimately, a generation of RAAF leaders emerged from the ranks of sergeant pilots and junior officers who underwent their baptism of fire on the Korean Peninsula. Using No 77 Squadron operations as a timeline, this concise history of the RAAF involvement in the war examines the roles of the transport unit, nurses, ground crews, prisoners of war and those who still have no known resting place.
The Frequency of Souls: A Novel
by Mary Kay ZuravleffA staid refrigerator designer's life is changed by a quirky, spiritual female colleague who is obsessed with finding electrical evidence of life after death in this extraordianry debut novel.
Designing Proximity: Reflections on Future Cities (Springer Series in Design and Innovation #45)
by Francesco Zurlo Laura GalluzzoThis book showcases nine possible scenarios for future cities, based on different aspects and characteristics of the term "proximity". Different points of view have been investigated on many themes related to the city of proximities: from bottom-up design actions to the inclusive city, from neighborhood services to public space in transformation, to platforms and economies of proximity. When discussing the concept of proximity, it is imperative to several aspects of building and inhabiting the city of fifteen minutes. The city and its neighborhoods are complex structures, made up of stratified levels of evolving systems, that encompass administrative and political aspects, urban spatial considerations, the dynamics of human interaction, and more. The necessity to re-appropriate the urban space leads all inhabitants to contemplate different aspects of their lives concerning proximity space, reflecting on how behavior, actions, and relationships can be improved and transformed to make our future more sustainable. This book envisions future scenarios that will make public space an active and functional place for the city, more inclusive, responding to the needs and desires of the different populations that inhabit it.
Retirement Portfolios: Theory, Construction, and Management (Wiley Finance #568)
by Michael J ZwecherA &“very practical&” guide for finance professionals on creating and managing retirement portfolios (Journal of Pensions, Economics and Finance). Retirement is one of the most important parts of the financial planning process, yet only two percent of financial advisors describe themselves as competent at it. But the demand is only growing as baby boomers move toward this new phase of life. It is imperative that financial advisors be equipped and ready. That's why Michael Zwecher—a leading expert on retirement income—has created Retirement Portfolios, which: Examines how portfolios should be prepped in advance so that the transition from &“working&” portfolio to retirement portfolio is smooth and seamless Outlines how to create a portfolio that will provide income, continue to generate growth, and protect assets from disaster Details the differences in managing a retirement portfolio versus managing portfolios during asset accumulation years The ability to create appropriate retirement portfolios and manage their risks are skills you must possess to be an effective financial advisor. Retirement Portfolios will help you develop these essential skills and gain a better understanding of the entire process.
A Technical Guide to Mathematical Finance (Chapman and Hall/CRC Financial Mathematics Series)
by Derek ZweigA Technical Guide to Mathematical Finance covers those foundational mathematical topics most important to an aspiring or professional quant. The text goes beyond a simple recitation of methods and aims to impart a genuine understanding of the fundamental concepts underpinning most of the techniques and tools routinely used by those working in quantitative finance.Features Suitable for professional quants and graduate students in finance, and mathematical/quantitative finance “Concept Refreshers” used throughout to provide pithy summaries of complex topics Step-by-step detail for formal proofs and mathematical descriptions