COURSE OVERVIEW: This course provides a review of basic arithmetic and continues through some of the early stages of algebra. Emphasis is placed on decimals, percentages and measurements, exponents, radicals and logarithms. Exercises are provided in factoring polynomials, linear equations, ratio, proportion and variation, complex numbers, and quadratic equations. The final assignment affords the student an opportunity to demonstrate what he or she has learned concerning plane figures, geometric construction and solid figures, and slightly touches on numerical trigonometry.
This book is a survey of abstract algebra with emphasis on linear algebra. It is intended for students in mathematics, computer science, and the physical sciences. The first three or four chapters can stand alone as a one semester course in abstract algebra. However they are structured to provide the background for the chapter on linear algebra. Chapter 2 is the most difficult part of the book because groups are written in additive and multiplicative notation, and the concept of coset is confusing at first. After Chapter 2 the book gets easier as you go along. Indeed, after the first four chapters, the linear algebra follows easily. Finishing the chapter on linear algebra gives a basic one year undergraduate course in abstract algebra. Chapter 6 continues the material to complete a first year graduate course. Classes with little background can do the first three chapters in the first semester, and chapters 4 and 5 in the second semester. More advanced classes can do four chapters the first semester and chapters 5 and 6 the second semester. As bare as the first four chapters are, you still have to truck right along to finish them in one semester.
Select and use appropriate technological tools, such as but not limited to spreadsheet, dynamic graphing tools, computer algebra systems, dynamic statistical package, graphing calculators, data collection software and presentation software to facilitate understanding of mathematical concepts
Remember though, that just because the book claims to be covering basicmathematics, that you won't be challenged. It can be tough, and especially when you're at the high school level, the mathematics won't seem like they're "basic", but more like, "hey, I just learned that last year/this year/whenever." It's ultimately a wonderful book if you're looking to strengthen the foundation of your mathematic ability, and Lang also includes a brief section after the first chapter about how you should logically examine math, which is invaluable.
The arrangement of major learning elements in Mathematics is now put into four content strands in every key stage, in total of twelve content strands. In every stage, four content strands are mutually related 2 . The same content strand names are not used to indicate progression beyond each stage. For example, in key stage 1, “Numbers and Operations”, Key Stage 2, Extension of Numbers and Operation and key stage 3, Numbers andAlgebra. The name of the content strands is progressing beyond the stages shows the extension and integration of content. In the case of measurement, key stage 1 relates with quantity and setting the units. In key stage 2, it extends to non-additive quantity beyond dimension. In Key stage 3, measurement is not used as one content strand because the idea of unit is embedded everywhere. For example, square root is an irrational number which means unmeasurable, Pythagorean theorem in geometry used for measuring, proportional function is used for counting the number of nails by weight, and in statistics, new measurements units are expressed such as quartile for boxplot.
The present set of notes was developed as a result of Higher Algebra courses that I taught during the academic years 1987-88, 1989-90 and 1991-92. The distinctive feature of these notes is that proofs are not supplied. There are two reasons for this. First, I would hope that the serious student who really intends to master the material will actually try to supply many of the missing proofs. Indeed, I have tried to break down the exposition in such a way that by the time a proof is called for, there is little doubt as to the basic idea of the proof. The real reason, however, for not supplying proofs is that if I have the proofs already in hard copy, then my basic laziness often encourages me not to spend any time in preparing to present the proofs in class. In other words, if I can simply read the proofs to the students, why not? Of course, the main reason for this is obvious; I end up looking like a fool.
Mata kuliah ini berbeda dengan matakuliah bahasa I nggris yang disajikan universitas, tidak membahas grammar ataupun writing secara khusus tetapi membahas vocabulary yang digunakan dalam matematika dan juga memberikan ketrampilan untuk mengajarkan matematika dalam bahasa I nggris. Matakuliah ini menekankan kepada kemampuan membaca dan membicarakan topik-topik matematika dalam bahasa I nggris. Secara umum materi BAHASA I NGGRI S MATEMATI KA meliputi I ntroduction; English for Algebra, English for Geometri, English for Statistics, English fo applied mathematics, English for classroom converstion, writing lesson plan. Kuliah ini sangat bermanfaat bagi mahasiswa dalam rangka menyiapkan diri untuk menjadi guru matematika di sekolah bilingual.
One of the easiest and most obvious ways to classify numbers is as either positive or negative. What does it mean for a number to be negative? Well, first of all, it is graphed to the left of the zero mark on a horizontal number line, but there’s more. A negative signifies the opposite of whatever is negated. For example, to say that I walked east 50 miles would be mathematically equivalent to saying that I walked west negative 50 miles. 2 I could also say that having a bank balance of -$41.90 is the same as being $41.90 in debt. The negative in mathematics represents a logical opposite. When two numbers are added, their values combine. When two numbers are multiplied, we perform repeated (or multiple) additions.
Groups are the central objects of algebra. In later chapters we will define rings and modules and see that they are special cases of groups. Also ring homomorphisms and module homomorphisms are special cases of group homomorphisms. Even though the definition of group is simple, it leads to a rich and amazing theory. Everything presented here is standard, except that the product of groups is given in the additive notation. This is the notation used in later chapters for the products of rings and modules. This chapter and the next two chapters are restricted to the most basic topics. The approach is to do quickly the fundamentals of groups, rings, and matrices, and to push forward to the chapter on linear algebra. This chapter is, by far and above, the most difficult chapter in the book, because all the concepts are new. Definition Suppose G is a non-void set and φ : G × G → G is a function. φ is called a binary operation, and we will write φ(a, b) = a · b or φ(a, b) = a +b. Consider the following properties.
Teachers and their development of teaching must be at the heart of any plan to improve educational systems. The Southeast Asian Ministers of Education Organization (SEAMEO) has uniquely represented the educational systems in the SEAMEO region with the collective aspirations of providing quality education for the next generation of leaders emphasising on science andmathematics education that underpins the agenda human resource needs of the region. Hence a framework and standards to support and improve the quality of science teachers is important for enhancing the standards of science education. Considering this, the SEAMEO Regional Centre for Education in Science andMathematics (RECSAM) has outlined the Southeast Asia Regional Standards for Science Teachers (SEARS-ST). Standards are statements of expectations of what the teachers should know and be able to do.
For the third indicators measured through three items test. The achievement mean obtained by student in this indicator is 22,58 or 59,42% of the maximum ideal score which is classified as medium category. From the achievement percentage can be seen that the students quite have been able to provide an explanation regarding the correctness of the result or answer a question. The results of interviews with some of students obtained the information that the students are not familiar with the form of the given problem. This is why they are confused about how to answer (how to explain the answers as instructed in the matter). From 18 students interviewed, some of them said that they only answer “that is the correct answer” or “that is not the correct answer”, while the description of the answer is simply written on paper graffiti. Then they were asked to answer again five test items that measure this indicator in accordance with the specified time and a half of them can be answered the questions completely and correctly. Upon further confirmed, it is known that the students are not familiar with these forms test. In the learning process, students are trained in solving routine problems that can be solved with regular formula given by the teacher.
In statistics, you’ll often come across the statement “correlation doesn’t imply causation.” This is a reminder that even if two sets of observations are strongly correlated with each other, that doesn’t mean one variable causes the other. When two variables are strongly correlated, sometimes there’s a third factor that influences both variables and explains the correlation. A classic example is the correlation between ice cream sales and crime rates—if you track both of these variables in a typical city, you’re likely to find a correlation, but this doesn’t mean that ice cream sales cause crime (or vice versa). Ice cream sales and crime are correlated because they both go up as the weather gets hotter during the summer. Of course, this doesn’t mean that hot weather directly causes crime to go up either; there are more complicated causes behind that correlation as well.
Salah satu masalah yang dihadapi dalam sistem pendidikan di Indonesia adalah rendahnya mutu pendidikan karena lemahnya proses pembelajaran. Proses pembelajaran mencakup metode, strategi, materi ajar, dan soal-soal latihan pendalaman materi. Dalam proses pembelajaran, banyak guru menyampaikan materi menggunakan metode konvensional dimana siswa hanya ditekankan untuk menghafal rumus. Sistem pembelajaran tersebut menyebabkan siswa belum mampu mencapai pemahaman materi yang maksimal. Pemahaman konseptual penting untuk dimiliki siswa. Tanpa pengetahuan konseptual dan kurang berkembangnya soal-soal yang disajikan dalam sebuah permasalahan kepada siswa , siswa akan kesulitan dalam memecahkan permasalahan pemahaman yang kompleks. Sehingga dibutuhkan pengembangan soal. Mengembangkan soal dengan menggunakan model Trends in International Mathematicsand Science Study (TIMSS) Pengembangan soal tersebut akan dikembangkan berdasarkan taksonomi Trends in Mathematicsand Science Study (TIMSS), yang bertujuan untuk meningkatkan kualitas mutu pendidikan di Indonesia.