Elements of Mathematics for Economists Bernard Cornet January 18‚ 2011 Contents Notation 1 Euclidean Spaces 1.1 Scalar Product and Associated Norm . . . . . . . . . . . . 1.1.1 Scalar Product . . . . . . . . . . . . . . . . . . . . 1.1.2 Norm Associated to a Scalar Product . . . . . . . . 1.1.3 Convergence in a Normed Space . . . . . . . . . . . 1.1.4 Euclidean Spaces and Hilbert Spaces . . . . . . . . 1.2 Matrices and Scalar Product . . . . . . . . . . . . . . . . . 1.2.1 Generalities on Matrices
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Algebra 1‚ most students enroll in this class their freshman year. A few special students take this class their eighth grade year. An even smaller pool of students are given the option to take this class their seventh grade year. Fortunately‚ I was part of the small group of students able to take Algebra 1 my seventh grade year. Not only did I make all A’s‚ but I also scored a pass plus on my ECAs for that class at a solid 729. The next year‚ I transferred schools where Geometry Honors was not offered
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Algebra II 7.3 Binomial Radical Expressions Radical expressions with the same index and the same radicand may be added or subtracted. Add or subtract: May need to simplify before adding or subtracting. Assignment: page 382383‚ #112 7.3 continued Multiplying Binomial Radical Expressions Use FOIL to multiply‚ simplify. Multiply: Conjugates are expressions such as: Just as (ab)(a+b) = a2b2 The product of conjugates is a rational number. Simplify: Assignment: page 382383‚ # 1322 7
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INTRODUCTION Abstract Algebra is more rightly considered meta-mathematics than mathematics proper‚ because it can be used to describe the structures that exist within mathematics from a general standpoint. The basic notions of Groups‚ Rings‚ Fields‚ and Algebraic Extensions provide a framework from which to examine almost all of mathematics. These notions serve as unifying concepts that interlace such seemingly disparate subjects as geometry‚ analysis‚ number theory‚ topology and even applied
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1. What is the exact number of bits in a memory that contains 640M bits? 640 · 1024 = 655‚360 · 1024 = 671‚088‚640 bits. 2. How many bits are in 1 Tb? You are asked to figure out the exact result. Hint: Depending on the tool used to calculate this‚ you may need to use a trick to get the exact result. Note that 220 = 1‚000‚00010 + d‚ where d is the difference between 220 and 1‚000‚00010‚ and that 1T = (1‚000‚00010 + d)2 8 bits/byte => 8 · 1 trillion or 812 => 8‚000‚000‚000‚000 3. Convert the binary
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MATH 1003 Calculus and Linear Algebra (Lecture 1) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 1003 1 / 18 Outline 1 About MATH 1003 2 Mathematics of Finance 3 Simple Interest Albert Ku (HKUST) MATH 1003 2 / 18 About MATH 1003 About MATH 1003 Lecturer: Albert Ku (Office: Rm 3492. E-mail: maybku@ust.hk) Teaching assistant: Dy Chun Yin‚ Li Xing‚ Lau Hing Sang and Wong Kwok Pang Office hours at Learning Commons: Fri 10:00-noon Textbook:
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Animal Kingdom The animal kingdom is a taxonomic kingdom composed of multicellular‚ eukaryotic organisms. Mostly‚ their body structures become fixed as they develop‚ yet still some organisms in this kingdom have the ability to undergo metamorphosis. The majority of these organisms are motile‚ which means they can move on their own and with spontaneity. All animals are heterotrophic‚ which implies that they depend on other organisms for food. Animals live in places that provide their necessities
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Direct Variation Try the following: 1. If m varies directly as y and m is 6 when y is 36‚ find the Choose: constant of variation. 1/6 6 1/36 36 Explanation 2. "a varies directly as b". If a = 3 when b = 24‚ find b when a = 10. Choose: 1.25 8 36 80 Explanation 3. There are about 200 calories in 50 grams of Swiss cheese. Choose: Willie ate 70 grams of this cheese. About how many 210 calories were in the cheese that he ate if the number of 240 calories
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The Use of Algebra in our Daily Life. 1. Algebra is a method of calculating using simple equations to represent quantity and to show relation between them. Algebra is also a part of our life‚ we use it on measuring the length of our table‚notebooks‚doors and other more. Another concept of mine is measuring capacity‚In school we always measure the right amount of ingredients that we cook. Because to an culinary student like me we are showing how to measure the exact amount of ingredients that
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1. The length of a rectangle is 4 feet less than twice the width of the rectangle. If the perimeter of the rectangle is 85 feet‚ find the width and the length. X L W x 2W-3 2. A total of $9000 is deposited into two simple interest accounts. In one account the annual simple interest rate is 5%‚ and in the second account the annual simple interest rate is 7%. The amount of interest earned for 1 year was $485. How much was invested in each account?
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