Bøger af Xing Zhou

This book is NOT the 2nd edition of the previous book C# in Front Office (ISBN: 144215358X). Instead, it covers many new topics and has lots of additional information. All contents in this book are chosen based on feedback, comments and questions from readers of the previous book. Some of the code samples in this book can be downloaded from the following address: http: //www.flexiblestudy.com/Site/Examples/CsInFrontOffic

An easy to follow guide to develop front office trading applications using C#.

Official site with more information and practice: www.mathallstar.org.Competition math is not about complicated theorems and formulas. It is more about how to analyze in order to solve challenging problems. Thus, merely remembering hundreds of theorems and formulas is far from sufficient to win math competitions. Students must be able to think effectively.This book aims to help students understand some frequently used methods of proof and improve their ability to think effectively. Contents in this book are organized based on methodologies rather than specific subjects. Consequently, examples and practice problems presented in each chapter may cover many different subjects. For example, the chapter Symmetry contains problems relating to polynomial factorization, equation, counting, and so on. Despite of being belong to different subjects, all of these problems can be solved by exploiting their intrinsic symmetric properties. Readers should focus on learning how to identify and utilize such properties. This analysis skill is a critical one to develop in addition to specific subject math knowledge.All the methodologies discussed in this book are intuitive and easy to understand. Some of them may be taught in classroom such as mathematical induction and proof by contradiction. Others may be not. Regardlessly, all of them are powerful to solve many competition problems. In addition, mastering the art of thinking not only is helpful for improving students' contest performance during school years, but also has positive impacts on their future. For example, some problems in this book originate from various job interviews. Being able to think effectively in order to solve such interview and other practical problems is certainly beneficial to their future.More information can be found at www.mathallstar.org.

There are hundreds of, if not more, geometry theorems. It is nearly impossible and definitely not necessary to remember all of them. Instead, students should focus on those must know theorems. In addition to remembering these theorems themselves, it is also important to study their typical applications. This book covers both areas.Each chapter of this book introduces a collection of related theorems. Those essential ones are discussed in the body contents. Students must remember all of them. Some additional theorems are included in the practice. They are good to know and remember.Practices are intended to demonstrate these theorems' typical applications. Many of them are classical problems. Some conclusion are well-known and can be practically treated as theorems. As such, students are encouraged to remember such conclusions as well.More information can be found at http: //www.mathallstar.org/

This book is not intended to replace an $1000$-page textbook which gives detailed lectures on every aspect of calculus. Instead, it is intended to explain core concepts in an intuitive way and to focus on practical perspectives of learning calculus.First, this book emphasizes on computational skills. The vast majority of students will use calculus as a computational tool in various scientific areas such as mathematics, physics, engineering, computer science, quantitative finance, and so on. Therefore, being able to correctly and quickly calculate derivatives, integrals etc is extremely useful and important to these students. Many calculus theorems are also covered. However, those overly abstract and academical details will be kept to a minimal. Such contents are very important to those students who are interested in pursuing pure mathematics. However, focusing too much on these topics may be a distraction to most other students.Another feature of this book is its focus on relations between calculus and various high school computational techniques such as trigonometric identities, polynomial transformation, and so on. Proficiency in using these techniques plays a vital role in solving many calculus problems. While these methods and formulas will be included in this book when they are needed, it is strongly recommended that readers should review these topics before attempting this book. Discussion of these techniques can be found in some Math All Star series books such as \textit{Power Calculation}, \textit{Trigonometry}, \textit{Competition Algebra}, and so on.Meanwhile, this book also includes many examples and applications in various subjects which use calculus. These include continuous compounded interest in finance, root finding algorithm in computer science, optimization in machine learning, and of course various applications in physics. This will help prepare students for applying their calculus skills in their future study and career. Finally, some selective historical competition problems are also included. These exercises provide students at different levels with an opportunity to test their problems solving skills that suit their individualized learning objective. Full solutions with detailed explanations are included.

Practice makes perfect. This book contains 100 problems focusing on binomial expansion (including multinomial expansion) and combinatorial identities (such as hockey stick identity, Vandermonde identity and so on). In addition to introducing these theorems and identities themselves, this book also discusses various typical problems and techniques that are related to these two topics. For more information, please visit https: //www.mathallstar.org/.

Practice makes perfect. This book contains over 150 MOD related problems with complete solutions aiming to polish students' competition skills. It also contains a review chapter which highlights all the important concepts, theorems and techniques. It is recommended that reader should use this book together with the book Number Theory (MOD) which is also part of the Math All Star series.

Official site with more information and practice: www.mathallstar.org.Remainder does not seem to be a big topic in school math. However, in competition math, it is. Almost every contest at middle school and high school level has remainder related problems. For example, in 2017 AMC 10B, out of total 25 problems, at least 3 are related to this topic: the 14th, 23rd, and 25th.Modular arithmetic is a branch in mathematics which studies remainders and tackles related problems. However, this important subject is not taught in schools. Consequently, many students rely on their intuition when attempting to solve such problems. This is clearly not the best situation.This book aims to provide a complete coverage of this topic at the level which is suitable for middle school and high school students. Contents will include both theoretical knowledge and practical techniques. Therefore, upon completion, students will have a solid skill base to solve related problems in math competitions.More information, including table of contents, pre-assessment etc, can be found at http: //www.mathallstar.org

Welcome to the Math All Star series! These books are for middle school and high school students who are motivated to participate in math competitions such as MathCounts, AMC, and AIME. Their coaches may also find these books useful.The website, http: //www.mathallstar.org, provides extra practice problems and serves as a highly recommended supplemental learning resource.Indeterminate EquationIndeterminate equations is a popular subject in math competitions at all levels, from AMC 8 to IMO. For example, in 2015 alone, both IMO and USAMO have an indeterminate equation problem out of 6 in total. Meanwhile, AIME and AMC12/10/8 also have various related questions.Despite its popularity, how to solve indeterminate equations is rarely discussed in classrooms. As a result, many students are lack of necessary knowledge and skills to tackle such problems. This book is to discuss various types of indeterminate equations and corresponding solving techniques. Upon completing this book, readers should be able to recognize and solve these indeterminate equations comfortably.Table of contents and pre-assessment are both available at the website www.mathallstar.com.

Official site with more information and practice: www.mathallstar.org.Trigonometry is an important subject in mathematics. It relates to many other subjects such as geometry, coordinate geometry, complex number, and so on. Therefore, trigonometric problems appear in almost every AMC12 or above competition either explicitly or implicitly. In addition, students attending lower level competition may find trigonometry can offer valuable alternative solutions to some geometry problems.In order to be proficient in trigonometry, it is necessary to memorize some formulas. However, there are hundreds, if not thousands, of trigonometric formulas. It is practically impossible and often unnecessary to remember all of them. Therefore, it is critical to know what formulas are essential and thus have to be remembered. Accordingly, the first objective of this book is to help students understand and remember those essential formulas.Remembering a sufficient number of formulas may help students achieve high scores in school tests. However, it is not sufficient to win math competitions. Students will have to master relevant techniques and be able to choose the most appropriate formula to solve particular problems. Let's take the following expression as an example: \begin{equation}\label{eq_ex}\cos 20^\circ \cos 40^\circ \cos 80^\circ\end{equation}\indent The value of this expression can be calculated in multiple ways. A classic technique is to multiply it by $\sin 20^\circ$. The result can be obtained by applying the double angle formula a few times. An alternative, relatively less known, solution is to apply the triple angle formula. This solution can produce the result immediately. Both approaches are workable in this case. Each of them can be used to tackle some generalized formed of \myJustRef{eq_ex}. As such, it is important for students to know all the relevant techniques and which one to choose in a particular case. Accordingly, the second objective of this book is to illustrate important techniques and to explain when to use them. In order to achieve this, some sample problems will appear repeatedly when different techniques are discussed. This will help students understand the pros and cons of different techniques when tacking specific problems.Upon completing this book, students should have the necessary basis for solving trigonometry problems in math competitions. In order to maximize learning results, students should attempt all the examples and practice problems once again after finishing the whole book. This will be helpful to re-enforce those techniques discussed and also offer a chance for students to reflect appropriateness of different techniques to solve particular problems

Being able to calculate correctly and efficiently is one of the most basic but important math skills. Therefore, it is not surprising to see various calculation problems in competitions at all levels.This book focuses on calculation skills. Contents are grouped by lectures. Each lecture features a classic problem. Many of such problems are not too hard to solve. However understanding how to solve these problems is just the very first step. It is more important to understand and master relevant calculation techniques. These techniques can help solve various problems of similar nature that will for sure appear in future math competitions.Readers should have basic algebraic knowledge and skills in order to appreciate the contents in this book. Some problems involve trigonometry and complex number. They can be safely skipped by those readers who are not familiar with these two subjects. Skipping certain topics will not affect learning other techniques contained in this book.Levels: MathCounts / AMC 8 - AMC 12 Table of contents, pre-assessment and more information can be found at http: //www.mathallstar.org

Welcome to the Math All Star series! These books are for middle school and high school students who are motivated to participate in math competitions such as MathCounts, AMC, and AIME. Their coaches may also find these books useful.The website, www.mathallstar.org, provides extra practice problems and serves as a highly recommended supplemental learning resource.CountingYou think everybody can count? Take a look at some counting problems available on the aforementioned website, and you might just think differently.Counting problems appear in all levels of math competitions. It is one type of problems that senior students and even adults may not necessarily do better on than well-trained junior students. This is because counting problems usually do not involve complex theorems or formulas. Rather, they demand a systematic and analytical approach, which can be mastered with the structured training that this book offers.The first half of the book teaches essential counting principles and formulas by going over easy-to-follow examples. After identifying hidden pitfalls and common misunderstandings, this book offers tips on how to avoid those traps. The second half covers well-established patterns in counting problems and introduces different ways to tackle each type. Mastering these techniques has proven to be very powerful and effective in improving problem solving skills.Each chapter starts with examples and progresses with inspiring questions, followed by detailed, step-by-step reasoning. When there are multiple solutions, their similarities and differences are examined to provide students with greater insights. Each chapter contains practice problems with full solutions provided at the end of the book.Upon completing this book, students will be able to: Analyze and approach problems like trained prosIdentify common pitfalls in problem solving, andRecognize frequently used patterns and apply appropriate techniques

Algebra is taught from elementary school to college and beyond. Algebraic problems present a significant portion in all math competitions including MathCounts, AMC, AIME, USAMO and so on. Therefore, solving competition level algebraic problems is a must-master skills for every contest contender.Algebra includes a wide range of topics and techniques. Some of them may be related to advanced mathematical theorems and tools. Therefore, it is impossible to cover all of them in one book. However, middle school and high school level competitions usually do not require advanced mathematics. Instead, the emphasis is on the applications of basic algebraic skills in a flexible and effective way to solve complex problems. As a result, it is a wise strategy to thoroughly understand the most important topics and drill down into details of related solving techniques in order to improve one's skill and test performance.This book covers three basic but important topics: equation, sequence and function. While these topics are all taught in schools, there are some competition specific techniques which deserve a systematic discussion. Taking Vieta's theorem as an example. While polynomial transformation is a well known method to evaluate expressions such as $x_1^2+x_2^2$, there are several other powerful techniques. They can be used to evaluate some complex expressions in a more efficient and less error-prone way. These expressions can have high power such as $x_1^{7}+x_2^{7}$, or are asymmetric such as $5x_1^3 + 3 x_2^5$. In fact, the latter asymmetric expression can present a challenge to many students who only know the polynomial transformation method. In addition to expression evaluation, Vieta's theorem can also be used to solve some seemingly unrelated problems. Such problems are among top hits in various math competitions.Sequence is another good example. Most students understand the two basic types of sequences, namely, arithmetic and geometric. Though the vast majority of sequence related problems in math contests can be converted to these basic types, finding such conversion may be a demanding task which is usually not discussed in classrooms. Meanwhile, in order to become a strong competitor, one must also understand a few additional more complex sequences especially those defined recursively. They are beyond the scope of school textbooks, but are discussed in this book.The goal of this book is to give an organized in-depth discussion on competition level techniques. Fully understanding these techniques will help students to quickly recognize and solve these types of problems. It will also lay down a solid foundation for them to solve other problems whose solutions require these algebraic techniques as critical stepping stones.Please visit http: //www.mathallstar.org/ for more information