Introduction to Technical Mathematics
... 52 - Remainder or Difference Unlike addition, the subtraction process is neither associative nor commutative. The commutative law for addition permitted reversing the order of the addends without changing the sum. In subtraction, the subtrahend and minuend cannot be reversed. a-b≠b–a Thus, the diffe ...
... 52 - Remainder or Difference Unlike addition, the subtraction process is neither associative nor commutative. The commutative law for addition permitted reversing the order of the addends without changing the sum. In subtraction, the subtrahend and minuend cannot be reversed. a-b≠b–a Thus, the diffe ...
Full text
... A2 , A3 , . . . the associated escalator number sequence. These concepts were first introduced by Pizá [3, 4, 5]. As shown in [2], an escalator sequence is uniquely determined by its base, a1 = A1 , and any rational number other than 1 is the base of an (infinite) escalator sequence. In this paper, ...
... A2 , A3 , . . . the associated escalator number sequence. These concepts were first introduced by Pizá [3, 4, 5]. As shown in [2], an escalator sequence is uniquely determined by its base, a1 = A1 , and any rational number other than 1 is the base of an (infinite) escalator sequence. In this paper, ...
Generalised Frobenius numbers: geometry of upper bounds
... problem. We aim to give an overview of the key results related to the scope of this thesis. For k = 2 it is well known (most probably at least to Sylvester [86]) that F(a1 , a2 ) = a1 a2 − (a1 + a2 ). Sylvester also found that exactly half of the integers between 1 and (a1 − 1)(a2 − 1) are represent ...
... problem. We aim to give an overview of the key results related to the scope of this thesis. For k = 2 it is well known (most probably at least to Sylvester [86]) that F(a1 , a2 ) = a1 a2 − (a1 + a2 ). Sylvester also found that exactly half of the integers between 1 and (a1 − 1)(a2 − 1) are represent ...
Modular curves, Arakelov theory, algorithmic applications
... This thesis is about arithmetic, analytic and algorithmic aspects of modular curves and modular forms. The arithmetic and analytic aspects are linked by the viewpoint that modular curves are examples of arithmetic surfaces. For this reason, Arakelov theory (intersection theory on arithmetic surfaces ...
... This thesis is about arithmetic, analytic and algorithmic aspects of modular curves and modular forms. The arithmetic and analytic aspects are linked by the viewpoint that modular curves are examples of arithmetic surfaces. For this reason, Arakelov theory (intersection theory on arithmetic surfaces ...
Lesson 1: The Pythagorean Theorem 8•7 Lesson 1
... Determine the positive square root of the number given. If the number is not a perfect square, determine which integer the square root would be closest to, then use “guess and check” to give an approximate answer to one or two decimal places. ...
... Determine the positive square root of the number given. If the number is not a perfect square, determine which integer the square root would be closest to, then use “guess and check” to give an approximate answer to one or two decimal places. ...
List of important publications in mathematics
This is a list of important publications in mathematics, organized by field.Some reasons why a particular publication might be regarded as important:Topic creator – A publication that created a new topicBreakthrough – A publication that changed scientific knowledge significantlyInfluence – A publication which has significantly influenced the world or has had a massive impact on the teaching of mathematics. Among published compilations of important publications in mathematics are Landmark writings in Western mathematics 1640–1940 by Ivor Grattan-Guinness and A Source Book in Mathematics by David Eugene Smith.