MSL is designed to prepare students, who have not met the criteria for entering programmes which require fundamental mathematical knowledge. It equips students without any prior maths background with the skills to be successful in entry level maths courses in all universities not only at Harbour.Space.
Why learning maths ? Mathematics opens the doors to many promising career paths.
Professional graduate schools (business, law, medicine) think it's a great major because they realize that studying mathematics develops analytical skills and the ability to work in a problem solving environment. Maths skills and experience rank high on their list of assets.
High salaries. The top 15 highest-earning college degrees have a common element: mathematics.
Job Satisfaction. In addition to higher pay, a maths major's employment promises higher levels of job satisfaction.
Jobs in the private sector abound:
Finance: Wall Street has become a major employer of maths majors.
Cryptography and Security: One area that is particularly "hot" these days is cryptography - the making and breaking of secret codes. Numerous businesses require cryptography. Banks employ cryptography in order to protect the privacy and integrity of their transactions. Number theory is the branch of pure mathematics which provides the theoretical underpinnings for much of the recent progress in cryptography.
Biotech: Recent breakthroughs in the study of DNA and proteins have generated a great deal of interest in mathematical biology. Many biotech companies hire mathematics majors because of the high (and growing) mathematical content of the field.
Computer and Data Science: The computer industry provides many lucrative jobs for maths majors.
Statements and predicates, sets and operations on them, quantifiers, mathematical induction, basics of combinatorics, Newton binomial, real numbers, equations and inequalities in one variable, equations and inequalities with modulus. Integer numbers: division with remainder, Euclidean algorithm, Euclidean algorithm, the greatest common divisor and least common multiple, relatively prime numbers, prime numbers, fundamental theorem of arithmetic. Definition of polynomial, method of undetermined coefficients, polynomial division with remainder, Bezout theorem, Vieta's theorem. Elements of information theory. Recurrence relations. Operators and expressions, linear bracket-free recording. Elements of graph theory.
The concept of the function. Ways of defining functions. Graph of the function. Some elementary functions. Some properties of functions. Graphical solution of equations and inequalities. Composition of functions. Inverse function. Elementary transformations of graphs of functions. Behavior of the function near the break points and at infinity. The concept of asymptote. The root of arbitrary degree. Generalization of the concept of degree. Logarithm.
The generalized concept of angle. Measuring angles in radians or degrees. The unit circle. Sine, cosine, arcsine, arccosine. Tangent, cotangent, arctangent, arccotangent. Trigonometric formulas. Method auxiliary argument. Trigonometric functions and their properties. Inverse trigonometric functions. Trigonometric equations.
Definition of complex numbers. Algebraic notation of complex numbers. Arithmetic operations on complex numbers. Complex numbers and polynomials. The fundamental theorem of algebra. Geometric representation of complex numbers. Trigonometric notation of complex numbers. The root of the complex number. Application of complex numbers. Random events. The classical definition of probability. The conditional probability. Independent events. The formula of total probability. Geometric probability.
The concept of sequence. Properties of sequence. Determination of the limit of the sequence. Properties of convergent sequences. Arithmetic operations on convergent sequences. Evaluation of the limits. The number e. Subsequences. Bolzano-Weierstrass theorem. The concept of limit of a function. Some properties of limits of the function. Calculating the limit of a function at a point. Classification of infinitely small functions. Continuity of functions. Properties of continuous functions on the interval. The existence and continuity of the inverse function. Asymptote of the graphics of the function.
Basic concepts and theorems of geometry. The emergence of the geometry out of the practice. Geometric shapes and body. Equality in geometry. Point, line and plane. The concept of locus of points. Distance. Segment, ray. Polyline. Angle. Right angle. Acute and obtuse angles. Vertical and adjacent angles. Bisector and its properties. Parallel and intersecting lines. Perpendicular lines. Theorems about parallel and perpendicular lines. Perpendicular and oblique to the line. Polygons. Circle. Visual representation of spatial bodies: the cube, parallelepiped, prism, pyramid, ball, sphere, cone, cylinder. Examples of cross-sections.
Triangle. Rectangular, sharp-angled, and obtuse triangles. Height, median, bisector, the middle line of the triangle. Isosceles and equilateral triangles; properties and characteristics of an isosceles triangle. Signs of equality of triangles. Triangle inequality. Sum of the angles of a triangle. The outer corners of the triangle. The relationship between the values of the sides and angles of a triangle. Intercept theorem. Similarity of triangles; similarity coefficient. Similarity of triangles. Pythagorean theorem. Signs of equality of right triangles. Sine, cosine, tangent, cotangent acute angle of a right triangle and the angles from 0 to 180. Pythagorean trigonometric identity. Formulas relating the sine, cosine, tangent, cotangent of the same angle. Cosine and sine theorem; examples of their application to calculate the elements of triangle. The point of intersection midperpendiculars, bisectors, medians.
Parallelogram, its properties and characteristics. A rectangle, square, rhombus, their properties and characteristics. Line, the middle line of the trapezoid; isosceles trapezoid. Polygons. Convex polygons. Sum of the angles of a convex polygon. Inscribed and circumscribed polygons. Regular polygons. Circle and circle. Measurement of geometric quantities. The length of the segment. The length of the broken line the perimeter of the polygon. Distance from point to line. The distance between the parallel lines. Circumference, pi; arc length. The angle. Degree measure the angle between the line length and the angle of the circular arc. The concept of the area of plane figures. Equipartitioned and of equal shape. The area of the rectangle. The area of a parallelogram, triangle and trapezoid (basic formulas). Formulas expressing the area of a triangle.
Computer Architecture. Architecture of Von Neumann's computer. Memory. Сomputer word. Half- adder and an adder. Bit arithmetic. Integer arithmetic. Real arithmetic. The file system. Basic operating system commands, utilities. batch processing operating system commands. Data control, data transmission protocols. Video memory and display devices. The history of computers.
The concept of the algorithm. Ways of describing the algorithm. The computational complexity of algorithms. Arrays. Dynamic programming. Search for an item in the vector. Strings. Exact search algorithms sample. Sorting vector. Sequence and files. Algorithms in number theory and computational algorithms. Combinatorial algorithms. Linear dynamic data structures. Trees. Dictionaries. Packaging data. The priority queue. Algorithms on graphs. Classical cryptography algorithms. Computational geometry algorithms. Alternative algorithmic system. Algorithmic strategies.
Development environment. The program code. The processing steps. The structure of the program. Console applications. Data typing. Simple types and operations on them. Bit arithmetic. Checksum machine word. Control structures. Debugging technology. Organization of input-output control input. Exchange algorithms. Components of the data structure. Sets: operations, problem solving. Functions and procedures. Implementation of recursion. Standard and custom modules / libraries. Strings and operations. Arrays: input and output, problem solving. Arrays: implementation of algorithms. Recording, processing and use. Pointers. Lists. Implementation structures "stack" and "turn". The implementation of binary search trees. Graphical tools programming system. Mechanisms animation implementation. Development of interfaces of user programs.
Procedural programming. Alternative programming paradigms. Object-oriented programming (objects and classes, collections and containers, the principles of object-oriented programming, computer modeling and animation features of object-oriented programming, criticism of object-oriented programing). Scripting languages (batch processing operating system commands). Markup languages (basic properties, cascading style sheet, page design, validation tools). Introduction to JavaScript. Stack-oriented programming language PostScript.