Mathematics in the General Education Core
The mathematics department provides three types of experiences for the general education core. The choice that a student and his/her advisor make will depend largely on the students major and interests. Each student should consult the Undergraduate Bulletin and speak with his/her advisor to determine the mathematics requirement(s) for his/her major. In broad, general terms, here are the courses which satisfy the general education core requirement in mathematics:
- MATH 1010 - Mathematical Thought and Practice
- MATH 1530 - Elements of Statistics
- MATH 1420 - Structure of Mathematical Systems II
- A course or courses in algebra and/or calculus.
- MATH 1110 - Algebraic Problem Solving
- MATH 1710 - Precalculus Algebra
- MATH 1730 - Precalculus
- MATH 1810 - Elements of Calculus
- MATH 1910 - Calculus I
Math 1010 -- Mathematical Thought and Practice
This course is designed specifically for students majoring in the arts and humanities. It deals with applications of mathematics in areas such as politics, code-breaking, art, music, and finance. (Did you know, for example, that the first presidential veto in U.S. history involved a mathematical formula?) MATH 1010 satisfies the general education core requirement in mathematics. It may be taken by any student whose major does not specify a particular math course. Students who enter APSU with ACT-M scores below 19 must enroll in an “E-section” of MATH 1010 or in an “E-section” of MATH 1530.
MATH 1530 -- Elements of Statistics
This is an introductory course in descriptive and inferential statistics. Students will learn things like how opinion polls are taken and how the margins of error for those polls are computed. Students will get an introduction to the ways in which statisticians decide if information from a sample can reasonably be used to infer information about a population. (These are the statistical methods, for example, that medical researchers use to determine if drugs or vaccines are effective.) MATH 1530 satisfies the general education core requirement in mathematics. Some majors require MATH 1530. Like MATH 1010, MATH 1530 may also be taken by any student whose major does not specify a particular math course. Students who enter APSU with ACT-M scores below 19 must enroll in an “E-section” of MATH 1010 or in an “E-section” of MATH 1530. Students with learning support requirements in reading or writing must satisfy these requirements prior to enrolling in Math 1530.
MATH 1420 – Structure of Mathematical Systems II
Topics include proportionality, the real number system, probability, data analysis, geometry, and measurement. Emphases are problem solving, multiplicative thinking, number sense, and communicating mathematics concepts with language, symbols, and concrete and pictorial representations. This course is reserved for students seeking elementary or middle school teaching licensure.
Algebra and/or Calculus
Several majors require courses in this category. Each course listed below satisfies the general education core requirement in mathematics. ACT requirements for each course can be seen in the table below. The courses in this category are:
- Algebra Courses: MATH 1110 (Algebraic Problem Solving) and MATH 1710(Precalculus Algebra) The primary difference between MATH 1710 and MATH 1110 is the instructional method employed. MATH 1710 is a more traditional lecture-based course. MATH 1110 classes involve more hands-on, activity-based learning strategies.
- Precalculus: MATH 1730 This course includes exponential and logarithmic functions and has a heavy emphasis on trigonometry.
- Calculus: MATH 1910 and MATH 1810 MATH 1810 is sometimes referred to as "Business Calculus." It does not require knowledge of trigonometry as a prerequisite. MATH 1910 does require proficiency in trigonometry as a prerequisite.
Placement in Algebra and Calculus Courses
Students whose major is within the fields of business, information systems, science, or mathematics follow the tracks listed below to fulfill their math general education requirement (although some majors require further math classes). Students may challenge their placement by taking (at their own expense) the APSU Mathematics Placement Examination.
History of Women in Mathematics
The field of mathematics has historically been dominated by men. Their names are famous: Euclid, the founder of geometry Pythagoras, whose theorem explains how to determine the area of a right triangle Archimedes, who discovered pi.
Well-known scientists like Albert Einstein (time and relativity) and Alan Turing (computer science) carried the torch in the 20th century. Meanwhile, even though math as a field of study remained largely closed to women, many women made significant contributions to algebra, geometry, theoretical math, and other areas of study.
Despite this, the gender gap in math persists across the professional spectrum of education and science. According to a study by the National Science Foundation, women accounted for only 28.5% of doctorates awarded in mathematics in the U.S. in 2016. This was a 4% increase from 1997 (24.1%), but a 1% decrease from 2006 (29.6%).
Headway has been made toward gender equity in math, but there’s still work to do.
Hypatia of Alexandria: One of the First Female Mathematicians
One of the earliest known women to make a major contribution to the field of mathematics was the Greek philosopher and educator Hypatia of Alexandria. She was born around 350, was an avowed paganist, and was killed by rioting monks in 415 or 416.
While none of her work survived the burning of the Library of Alexandria, subsequent writings about her credited her or her Neoplatonic students with inventing vital measurement, observation, and navigation tools, such as the plane astrolabe, the graduated brass hydrometer, and the hydroscope.
According to the ThoughtCo encyclopedic entry on Hypatia of Alexandria, she’s believed to have lectured on and written about the motions of the planets, number theory, and conic sections.
She’s become a symbol of feminism. Her unsuccessful effort to preserve the knowledge contained in the ancient library was the subject of the 2009 movie “Agora,” starring British-born actor Rachel Weisz as Hypatia.
Hypatia of Alexandria: Resources
During the Renaissance and Age of Enlightenment, mathematical, scientific, and artistic advancements of men, such as Nicolaus Copernicus, Rene Descartes, Leonardo da Vinci, Gottfried Wilhelm Leibniz, and Sir Isaac Newton, grabbed the spotlight. As in most academic fields during that time, women had limited access to the tools of learning and research.
During the 1700s and 1800s, a number of women began to make their marks on the field of mathematics. Women published textbooks, conducted groundbreaking research, and translated ancient mathematical works from Latin and Greek.
Not until the 20th century would women be widely accepted as equals in the male-dominated field. In 2019, Karen Uhlenbeck was awarded one of math’s greatest honors, the Abel Prize this was the first time that a woman had been given this honor. However, even as societal attitudes shifted in the direction of gender equity, many barriers remained for women in mathematics.
Women In Math: By the Numbers
Academic studies and statistical analyses of the gender inequity in math are clear: Female mathematicians remain at a distinct and systemic disadvantage.
According to salary information compiled by the National Science Foundation, female mathematical scientists earned $70,000, on average, in 2017. Men in the same field with comparable experience earned $81,000, meaning for every dollar earned by a male math scientist, a female math scientist earned 86 cents.
A 2018 survey by the American Mathematical Society found that only 31% of math positions in higher education were filled by women, including 30% of all tenure-track positions.
Another indication of the relative lack of agency of women in mathematics is the large gender gap among members of editorial boards of academic journals. According to “Why Are There So Few Women Mathematicians?,” mathematician Chad Topaz and computer scientist Shilad Sen discovered that only 9% of editorial board positions were held by women.
This relative lack of representation among the informational gatekeepers of the field is evidence of ongoing gender disparity in mathematics.
Resources may contain links to sites external to the EngageNY.org website. These sites may not be within the jurisdiction of NYSED and in such cases NYSED is not responsible for its content.
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This two-year programme reflects the versatility of mathematics and focuses on questions from all major branches of advanced modern mathematics, pure as well as applied. It allows you to specialise in the area of your interest, while broadening your knowledge in general. Specifically, you choose one of the four specialisations, each offering a large number of courses.
A large and varied blend of local UvA courses and MasterMath courses
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Section 1: Algebra and Decimals
Duration: 35 hours, 18 minutes
Number of Lessons: 80
This course is perfect for 5th or 6th graders currently taking mathematics, or for anyone looking to perfect previous math skills.
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24.1: YouTube - Mathematics
- Discrete Probability Distribution – If the probabilities are defined on a discrete random variable, one which can only take a discrete set of values, then the distribution is said to be a discrete probability distribution. For example, the event of rolling a die can be represented by a discrete random variable with the probability distribution being such that each event has a probability of .
- Continuous Probability Distribution – If the probabilities are defined on a continuous random variable, one which can take any value between two numbers, then the distribution is said to be a continuous probability distribution. For example, the temperature throughout a given day can be represented by a continuous random variable and the corresponding probability distribution is said to be continuous.
Cumulative Distribution Function –
Similar to the probability density function, the cumulative distribution function of a real-valued random variable X, or just distribution function of evaluated at , is the probability that will take a value less than or equal to .
For a discrete Random Variable,
For a continuous Random Variable,
Uniform Probability Distribution –
The Uniform Distribution, also known as the Rectangular Distribution, is a type of Continuous Probability Distribution.
It has a Continuous Random Variable restricted to a finite interval and it’s probability function has a constant density over this interval.
The Uniform probability distribution function is defined as-
Expected or Mean Value – Using the basic definition of Expectation we get –
Variance- Using the formula for variance-
Standard Deviation – By the basic definition of standard deviation,
- Example 1 – The current (in mA) measured in a piece of copper wire is known to follow a uniform distribution over the interval [0, 25]. Find the formula for the probability density function of the random variable representing the current. Calculate the mean, variance, and standard deviation of the distribution and find the cumulative distribution function .
- Solution – The first step is to find the probability density function. For a Uniform distribution, , where are the upper and lower limit respectively.
The expected value, variance, and standard deviation are-
The cumulative distribution function is given as-
There are three regions where the CDF can be defined,
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24.1: YouTube - Mathematics
Eigen vector of a matrix A is a vector represented by a matrix X such that when X is multiplied with matrix A, then the direction of the resultant matrix remains same as vector X.
Mathematically, above statement can be represented as:
where A is any arbitrary matrix, λ are eigen values and X is an eigen vector corresponding to each eigen value.
Here, we can see that AX is parallel to X. So, X is an eigen vector.
Method to find eigen vectors and eigen values of any square matrix A
We know that,
Above condition will be true only if (A – λI) is singular. That means,
(2) is known as characteristic equation of the matrix.
The roots of the characteristic equation are the eigen values of the matrix A.
Now, to find the eigen vectors, we simply put each eigen value into (1) and solve it by Gaussian elimination, that is, convert the augmented matrix (A – λI) = 0 to row echelon form and solve the linear system of equations thus obtained.
Eigen values of real symmetric and hermitian matrices are real
Eigen values of real skew symmetric and skew hermitian matrices are either pure imaginary or zero
Eigen values of unitary and orthogonal matrices are of unit modulus |λ| = 1
Eigen values of A = Eigen Values of A T (Transpose)
Sum of Eigen Values = Trace of A (Sum of diagonal elements of A)
Product of Eigen Values = |A|
Maximum number of distinct eigen values of A = Size of A
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