Encyclopedia of Mathematics is a comprehensive one-volume encyclopedia designed for high school through early college students. More than 1,000 entries, numerous essays, and more than 125 photographs and illustrations cover the principal areas and issues that characterize this "new" area of science. This valuable resource unites disparate ideas and provides the meaning, history, context, and relevance behind each one. The easy-to-use format makes finding straightforward and natural answers to questions within arithmetic simple. Encyclopedia of Mathematics also gives historical context to mathematical concepts, with entries discussing ancient Arabic, Babylonian, Chinese, Egyptian, Greek, Hindu, and Mayan mathematics, as well as entries providing biographical descriptions of important people in the development of mathematics.
A playful, readable, and thorough guide to precalculus, this book is directed at readers who would like a holistic look at the high school curriculum material on functions and their graphs. The exploration is presented through problems selected from the history of the Mathematical Association of America's American Mathematics Competition.
This guide covers the story of trigonometry. It is a swift overview, but it is complete in the context of the content discussed in beginning and advanced high-school courses. The purpose of these notes is to supplement and put into perspective the material of any course on the subject you may have taken or are currently taking. (These notes will be tough going for those encountering trigonometry for the very first time!)
This book is a collection of 34 curiosities, each a quirky and delightful gem of mathematics and each a shining example of the joy and surprise that mathematics can bring. Intended for the general math enthusiast, each essay begins with an intriguing puzzle, which either springboards into or unravels to become a wondrous piece of thinking. The essays are self-contained and rely only on tools from high-school mathematics (with only a few pieces that ever-so-briefly brush up against high-school calculus). The gist of each essay is easy to pick up with a cursory glance—the reader should feel free to simply skim through some essays and dive deep into others. This book is an invitation to play with mathematics and to explore its wonders. Much joy awaits! In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Mathematics Galore! Showcases some of the best activities and student outcomes of the St. Mark's Institute of Mathematics and invites you to engage the mathematics yourself! Revel in the delight of deep intellectual play and marvel at the heights to which young scholars can rise. See some great mathematics explained and proved via natural and accessible means. Based on 26 essays ( newsletters ) and eight additional pieces, Mathematics Galore! offers a large sample of mathematical tidbits and treasures, each immediately enticing, and each a gateway to layers of surprising depth and conundrum. Pick and read essays in no particular order and enjoy the mathematical stories that unfold. Be inspired for your courses, your math clubs and your math circles, or simply enjoy for yourself the bounty of research questions and intriguing puzzlers that lie within.
This book is a collection of 34 curiosities, each a quirky and delightful gem of mathematics and each a shining example of the joy and surprise that mathematics can bring. Intended for the general math enthusiast, each essay begins with an intriguing puzzle, which either springboards into or unravels to become a wondrous piece of thinking. The essays are self-contained and rely only on tools from high-school mathematics (with only a few pieces that ever-so-briefly brush up against high-school calculus). The gist of each essay is easy to pick up with a cursory glance--the reader should feel fre.
Thoroughly revised and expanded, this is the definitive reference on American immigration from both historic and contemporary perspectives. It traces the scope and sweep of U.S. immigration from the earliest settlements to the present, providing a comprehensive, multidisciplinary approach to all aspects of this critically important subject. Every major immigrant group and every era in U.S. history are fully documented and examined through detailed analysis of social, legal, political, economic, and demographic factors. Hot-topic issues and controversies - from Amnesty to the U.S.-Mexican Border - are covered in-depth. Archival and contemporary photographs and illustrations further illuminate the information provided. And dozens of charts and tables provide valuable statistics and comparative data, both historic and current. A special feature of this edition is the inclusion of more than 80 full-text primary documents from 1787 to 2013 - laws and treaties, referenda, Supreme Court cases, historical articles, and letters.
Marson and Ferris' Business Law provides a thorough account of the subject for students on Business degrees. It introduces students to the essential topics by exploring current and pertinent examples. It emphasizes the importance of cases and demonstrates the relevance of the law in a business environment.
Bilingualism is a reality that many Americans still find difficult to accept; hence the prominence of English-only activism in U.S. politics. This collection of essays analyzes the sources of the anti-bilingual movement, its changing directions, and its impact on education policy. The book also explores efforts to resist the English-only trend, including projects to revitalize Native American languages.
The Taxation of Small Businesses 2022-23 is a practical guide to all aspects of direct taxation of small businesses in one volume. It is ideal for sole practitioners and small partnerships, but will be a handy reference guide for all tax advisers. The book aims to give a clear explanation of the relevant legislation and practical advice on ways of minimising clients’ tax liabilities and warning against common pitfalls. The fourteenth edition has been updated to incorporate changes as a result of the Finance Act 2022.
In What Photography Is, James Elkins examines the strange and alluring power of photography in the same provocative and evocative manner as he explored oil painting in his best-selling What Painting Is. In the course of an extended imaginary dialogue with Roland Barthes's Camera Lucida, Elkins argues that photography is also about meaninglessness--its apparently endless capacity to show us things that we do not want or need to see--and also about pain, because extremely powerful images can sear permanently into our consciousness. Extensively illustrated with a surprising range of images, the book demonstrates that what makes photography uniquely powerful is its ability to express the difficulty--physical, psychological, emotional, and aesthetic--of the act of seeing.
The Taxation of Small Businesses 2023-24 is a practical guide to all aspects of direct taxation of small businesses in one volume. It is ideal for sole practitioners and small partnerships, but will be a handy reference guide for all tax advisers. The book aims to give a clear explanation of the relevant legislation and practical advice on ways of minimising clients’ tax liabilities and warning against common pitfalls. The sixteenth edition has been updated to incorporate changes as a result of the Finance Act 2023. Contents List of abbreviations Chapter 1. Income Tax Computation 1.1. Aggregation of Taxpayer’s Income 1.2. Interest 1.3. Limit on Deductions from Adjusted Net Income 1.4. Payments to Charities 1.5. Personal Allowances Deducted from Net Income 1.6. Computation of Tax 1.7. Tax Reducers 1.8. Tax Retained on Interest, Royalties and Gift Aid donations 1.9. Comprehensive Example 1.10. Death and Separation 1.11. Married Couples – Joint Property 1.12. Minor Children 1.13. High Income Child Benefit Charge Chapter 2. Taxation of Trading Income 2.1. Introduction 2.2. Statutory Definitions of Trading 2.3. Statutory Trades 2.4. Case Law 2.5. Gambling and Speculation 2.6. Illegal Activities 2.7. Individuals Trading in Shares 2.8. Definition of Trading – National Insurance 2.9. Mutual Trading 2.10. Election to Use Cash Basis 2.11. Capital and Revenue Receipts 2.12. Receipts not Received in Course of Trade 2.13. Other Receipts 2.14. Capital and Revenue Payments 2.15. Expenditure Incurred in the Course of a Trade 2.16. Duality of Purpose 2.17. Repairs and Maintenance 2.18. Replacement of Assets 2.19. Depreciation and Amortisation 2.20. Subscriptions and Donations 2.21. Sponsorship 2.22. Bad Debts 2.23. Provisions 2.24. Payments to Employees & Appropriations of Profit 2.25. Entertainment 2.26. Gifts to Customers and Samples 2.27. Gifts to Educational Establishments and Charities 2.28. Cost of Leasing Cars 2.29. Legal and Professional Fees 2.30. Fines and Payments Against the Public Interest 2.31. Interest and Bank Charges 2.32. Pre-trading Expenditure 2.33. Indirect Taxation 2.34. Compensation and ex gratia Payments to Former Employees 2.35. Redundancy Payments 2.36. Removal Expenses to New Business Premises 2.37. Premiums for Insurance 2.38. Payments to Employees for Restrictive Undertakings 2.39. Staff Training and Development 2.40. Counselling Courses in Connection with Termination of Employment 2.41. Payments to Secure Release from Unprofitable Contracts 2.42. Payments to Political Parties 2.43. Preservation of Goodwill 2.44. Payments on the Cessation of Trade 2.45. Post-cessation Expenditure 2.46. Rent 2.47. Lease Premium 2.48. Patents and Intellectual Property 2.49. Telephone 2.50. Business Rates and Council Tax 2.51. Security Expenditure 2.52. Loan Guarantee Payments 2.53. Use of Home 2.54. Website Expenditure 2.55. Expenses Connected with Foreign Trades 2.56. Valuation of Stock 2.57. Overseas Aspects of Trading Chapter 3. Capital Allowances on Plant and Machinery 3.1. Introduction 3.2. Definition of Plant and Machinery 3.3. Assets Deemed to be Plant and Machinery 3.4. Definition of Expenditure 3.5. Date of Expenditure 3.6. Disposal of Assets 3.7. Allowances 3.8. Calculation of Capital Allowances 3.9. Short-life Assets 3.10. Cessations and Successions 3.11. Hire Purchase and Leasing 3.12. Fixtures 3.13. Disposal of Fixtures 3.14. Anti-avoidance Chapter 4. Other Allowances 4.1. Business Premises Renovation Allowance 4.2. Patents 4.3. Know-how Chapter 5. Basis Periods 5.1. Current Year Basis (CYB) 5.2. Opening Year Rules 5.3. Closing Year Rules 5.4. Tax Planning on Commencement 5.5. Tax Planning on Cessation 5.6. Change of Accounting Date 5.7. Period Less than 12 Months 5.8. Period More Than 12 Months 5.9. Two Accounting Dates in Tax Year 5.10. No Accounting Date in Tax Year 5.11. Transitional Overlap Relief 5.12. Changes in Size and Nature of Operations 5.13. Death of Trader 5.14. Mergers and Demergers 5.15. Date of Commencement and Cessation 5.16. Successions 5.17. Trader Becoming, or Ceasing to be, UK Resident Chapter 6. Trading Losses 6.1. Introduction 6.2. Offset Against Future Trading Income 6.3. Transfer of Business to a Company 6.4. Offset Against Total Income and Carry-back 6.5. Offset Against Capital Gains 6.6. Losses in the Early Years of Trading 6.7. Terminal Loss Relief 6.8. Tax Planning and Loss Relief 6.9. Restriction of Loss Relief 6.10. Late Claims Chapter 7. Property Income 7.1. Introduction 7.2. Basis of Assessment 7.3. Dilapidations 7.4. Lease Premiums 7.5. Sale with Right of Conveyance 7.6. Expenditure Deductible 7.7. Sea Walls 7.8. Mutual Business 7.9. Relief for Capital Expenditure 7.10. Losses 7.11. Furnished Holiday Lettings 7.12. Rent a Room Scheme Chapter 8. Employment and Self-employment 8.1. Introduction 8.2. Benefits of Self-employment 8.3. Definition of Employment and Self-employment 8.4. Tests for Employment 8.5. Workers Supplied by Agencies 8.6. Non-executive Directors 8.7. Self-employment or a Number of Separate Employments 8.8. Provision of Services Through an Intermediary – Income Tax 8.9. Managed Service Companies 8.10. National Insurance – Deemed Employment 8.11. National Insurance – Deemed Self-employment 8.12. National Insurance – Persons Deemed not to be Employed Chapter 9. Employment Income 9.1. Income Tax – Introduction, Charging Legislation and General Definitions 9.2. National Insurance Contributions – Charging Legislation and General Definitions 9.3. Income Tax and National Insurance – a Comparison 9.4. Time of Receipt 9.5. Cash Payments to Employees 9.6. Payments Arising by Reason of Employment 9.7. Payments on Termination of Employment or Variation of Employment Terms 9.8. Damages and Compensation Paid to Employee 9.9. Sick Pay and Sickness and Other Benefits 9.10. Commission, Cashbacks and Discounts 9.11. Tax-free Lump Sum Payments 9.12. Payment of Expenses to Third Parties on Behalf of Employee 9.13. Payments for Clothing 9.14. Directorships Held by Partners 9.15. Payment of Employee’s Tax by Employer 9.16. Income Tax – Deduction of Expenses 9.17. Reimbursement of Expenses 9.18. Qualifying Travel Expenses 9.19. Entertainment 9.20. Expenses Incurred by Homeworkers 9.21. Other Deductible Expenses 9.22. Payments and Benefits Exempt from Income Tax and Class 1 National Insurance Contributions Chapter 10. Benefits in Kind 10.1. Valuation of Benefits in Kind 10.2. Benefits – Definition of Cost 10.3. Lower-paid Employment 10.4. Benefits in Kind and National Insurance Contributions 10.5. Payment of Expenses by Employer 10.6. Gift of Assets to Employees 10.7. Cash Vouchers, Non-cash Vouchers and Credit Tokens 10.8. Payment Made to a Registered Pensions Scheme for the Benefit of Two or More People 10.9. Waiver of Loan 10.10. Job-related Accommodation 10.11. Assets Available for Private Use 10.12. Expenses Connected with Living Accommodation 10.13. Cars 10.14. Fuel for Private Use 10.15. Pool Cars and Vans 10.16. Vans and Heavier Commercial Vehicles 10.17. Emergency Vehicles 10.18. Beneficial Loans 10.19. Scholarships 10.20. Relocation Packages and Guaranteed Selling Price Schemes 10.21. Medical Treatment and Medical Insurance Chapter 11. National Insurance Contributions National Insurance Contributions and Employees 11.1. Earnings Period 11.2. Aggregation of Earnings 11.3. Rate of Class 1 National Insurance Contributions 11.4. Class 1A Contributions 11.5. Calculation of Contributions 11.6. Class 1A Charge Where Benefits Provided by Third Parties 11.7. Earners over Pensionable Age 11.8. Notional Payments of Class 1 Contributions 11.9. Annual Maximum Contributions National Insurance Contributions and the Self-Employed 11.10. Class 2 Contributions 11.11. Class 4 Contributions Chapter 12. Pensions 12.1. Introduction 12.2. Scope of Regime 12.3. Registration of Pension Schemes 12.4. Payments by Registered Pension Schemes 12.5. Pension Payments 12.6. Contributions 12.7. Purchase of Shares in Sponsoring Employer 12.8. Loans to Employers 12.9. Unauthorised Payments Charge Chapter 13. Capital Gains Tax 13.1. Scope of Capital Gains Tax (CGT) 13.2. Exemptions 13.3. Residence 13.4. Capital Losses 13.5. Offset of Trading and Other Losses against Capital Gains 13.6. Capital Gains Tax Rate 13.7. Disposal Consideration 13.8. Date of Disposal 13.9. Allowable Costs 13.10. Indexation Allowance 13.11. Taper Relief 13.12. Assets Owned at 31 March 1982 13.13. Married Couples and Civil Partners 13.14. Disposal to Connected Parties 13.15. Valuation of Assets 13.16. Negligible Value Claim 13.17. Value Shifting 13.18. Disposal by Way of Security 13.19. Hire Purchase Transactions 13.20. Appropriations to and from Trading Stock 13.21. Series of Transactions 13.22. Options 13.23. Debts 13.24. Compensation 13.25. Asset Derived from another Asset 13.26. Location of Assets 13.27. Chattels and Wasting Assets 13.28. Part Disposals 13.29. Leases 13.30. Loss or Destruction of Asset 13.31. Restoration of Assets 13.32. Replacement of Business Assets 13.33. Gift Relief 13.34. Transfer of Assets to a Limited Company 13.35. Entrepreneurs’ Relief 13.36. Losses on Loans to Traders 13.37. Loan Guarantees Chapter 14. Corporation Tax 14.1. Scope of Corporation Tax 14.2. Trading income 14.3. Loan relationships 14.4. Intangible Fixed Assets 14.5. Derivative Contracts 14.6. Property income 14.7. Chargeable gains 14.8. Indexation Allowance 14.9. Indexation and Losses 14.10. Assets Owned at 31 March 1982 14.11. Assets Owned at 6 April 1965 14.12. Rollover Relief 14.13. Dividends Received 14.14. Payments to Charities 14.15. Distributions 14.16. Chargeable Accounting Periods 14.17. Computation of Tax Liability 14.18. Corporation Tax – Interaction with Income Tax 14.19. Losses and Corporation Tax 14.20. Groups and Consortia 14.21. Close Companies 14.22. Companies with Investment Business 14.23. Close Investment-holding Companies 14.24. Demergers 14.25. Purchase of Own Shares Chapter 15. Incorporation, Disincorporation and Choice of Business Medium 15.1. Introduction 15.2. Incorporation 15.3. Disincorporation 15.4. Disincorporation Relief 15.5. Choice of Business Medium 15.6. Comparison of Tax Treatment of Companies and Sole Traders 15.7. Salary vs Dividends Chapter 16. Special Classes of Taxpayers 16.1. Construction Industry Scheme 16.2. Farmers and Market Gardeners 16.3. Authors, Artists and Composers 16.4. Actors, Musicians and Entertainers 16.5. Entertainers – Other Workers 16.6. Builders 16.7. Care Providers 16.8. Barristers 16.9. Bookmakers 16.10. Breweries and Licensed Premises 16.11. Doctors and Dentists 16.12. Motor Dealers – Valuation of Used Vehicle Stocks 16.13. Fishermen 16.14. Franchising 16.15. Solicitors 16.16. Sub-postmasters 16.17. Video and DVD Traders 16.18. Clubs, Societies and other Mutual Organisations 16.19. Charities 16.20. Credit Unions 16.21. Friendly Societies 16.22. Housing Associations 16.23. Self-build Societies Chapter 17. Partnerships 17.1. Definitions 17.2. Limited Partnerships 17.3. Limited Liability Partnerships 17.4. Allocation of Profits 17.5. Assessment of Partnerships 17.6. Other Income of Partnership 17.7. Non-trading Partnerships 17.8. Post-cessation Receipts 17.9. Losses 17.10. Notional Losses 17.11. Mergers and Amalgamations 17.12. Restriction on Loss Relief for Limited and Non-Active Partners 17.13. Partnership Property Income 17.14. Corporate Partners 17.15. Partnerships and Capital Gains Tax 17.16. Roll-over and Gift Relief - LLPs Index
Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.
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