We can provide help in any branch of Mathematics, at any level. This includes helping students solve difficult assignments in various Undergraduate & Postgraduate University Courses. Below we provide a non-exhaustive list of University Courses with advanced mathematical content, that we regularly provide help with.

• Real numbers
• Axiom of completeness
• Sequences & Convergence
• Functions
• Limits & Continuity
• Intermediate Value Theorem
• Continuous functions
• Monotone functions
• Algebraic, Exponential, Logarithmic functions
• Derivative
• Differentiation Rules
• Mean Value Theorems
• Countable & Uncountable Sets

• Subsequences
• Bolzano-Weierstrass Theorem
• Supremum & Infimum
• Cauchy sequences
• Series & Convergence
• Uniform continuity
• Convex & Concave functions
• Riemann Integral: Definition & Properties
• Mean-Value Theorems
• Fundamental Theorem of Calculus
• Integration techniques
• Taylor's Theorem
• Power Series

• Vector Calculus in 3-D Euclidean space:
  Vectors, Scalar Product, Cross Product & Applications
• Analytic Geometry in 3-D Euclidean space:
  Planes, Curves, Surfaces, Cylindrical coordinates & Spherical coordinates
• Linear Algebra of Euclidean Space:
  Algebraic structure, Matrices & Linear Mappings
• Topology of Euclidean Space:
  Sequences, open & closed sets, bounded & compact sets, connected sets
• Functions of several variables:
  Limits & Continuity, Fundamental Theorems for continuous functions, Uniform Continuity.
• Differentiability of functions of several variables:
  Partial derivatives, gradient, differential, tangent plane, linearization.
• Main Theorems of Differential Calculus:
  Chain Rule, Inverse & Implicit function theorem
• Maxima & Minima
• Applications of Differential Calculus
• Double & Triple Integrals:
  - definition & properties 
  - Area & Volume 
  - Integration techniques 
  - Change of variables 
  - Transformations (Polar, cylindrical & spherical)
• Line Integrals:
  - definition, properties & computation 
  - parameterized curves 
  - length of a curve 
  - applications
• Surface Integrals:
  - definition & properties
  - computations & applications
• Vector Analysis:
  - differential operators of scalar & vector fields
  - Green's theorem & Stoke's theorem
  - divergence theorem & applications

• Basic counting principles
• Sums & products
• Recursive relations
• Permutations & Combinations
• Divisions & Partitions of a finite set
• Integer solutions of linear equations
• Binomial & multinomial coefficients
• Computations of finite sums
• The Inclusion-Exclusion principle
• Generating Functions for combinations & permutations
• Distributions & occupancy

• Basic principles of enumeration (enumeration of sets, words, permutations)
• Binomial Coefficients & properties
• Ordinary & Exponential Generating Functions
• Applications of Generating Functions in enumerating sets, permutations, partitions of integers & sets
• Special numbers: Stirling, Bell, Catalan
• The principle of Inclusion-Exclusion
• Recurrence relations & difference equations
• Computation of Sums
• The Pigeonhole Principle
• Applications in problems of enumeration of graphs:
  - enumeration of matchings and colorings
  - Euler's formula for planar graphs
  - Cayley's formula for the number of trees
• Graph Theory
• Extremal combinatorics
• Discrete Geometry
• Polya's Theory
• Analytic Combinatorics

• Isomorphisms & Automorphisms
• Transformations & relations on graphs
• Degrees, density, min-max theorem
• Paths, cycles, diameter, radius, center, perimeter
• Connectivity
• Trees, forests & spanning trees
• Planar graphs, duality, density & planarity
• Graph coloring
• Bipartite graphs, coloring & degeneracy
• Cliques, Independent sets, Ramsey numbers
• Coverings & Matchings
• Euler cycles & Hamilton cycles

• Hypothesis Tests
• Non-parametric inference
• Linear Models
• Analysis of Variance

• Matrices
• Systems of Linear Equations
• Linear Mappings
• Determinants

• Determinants
• Polynomials
• Eigenvalues & Eigenvectors
• Linear Transformations (Diagonalizable & Triangulable)
• The Cayley-Hamilton Theorem
• Minimal Polynomial
• Primary Decomposition
• Jordan Canonical Form
• The standard Inner Product
• Unitary & Hermitian Matrices
• Quadratic Forms

• Vector Calculus
• Coordinate Geometry in the xy-plane
• Analytic Geometry in 3-dimensional space
• Euclidean Geometry in n-dimensional space

• Descriptive Statistics
• Distribution Families
• Sufficiency & Completeness
• Minimum Variance Unbiased Estimators
• Efficient & Consistent Estimators
• Maximum Likelihood Estimators (MLEs)
• Moment Estimators
• Bayes & Minimax Estimators
• Confidence Intervals
• Hypothesis Testing

• Complex numbers
• Topology of metric spaces
• Holomorphic functions
• Cauchy-Riemann equations
• Power series
• Taylor's theorem
• Complex Integration
• Cauchy Integral Theorem
• Maximum principle
• Morera Theorem
• Liouville Theorem
• Fundamental Theorem of Algebra
• Analytic continuation
• Sequences of holomorphic functions
• Poles & roots
• Laurent series
• Residue theorem
• Computations of Improper integrals

• Prime Numbers
• The Fundamental Theorem of Arithmetic
• Divisibility, GCD, LCM, Euclid's Algorithm
• Linear Diophantine equations
• Pythagorean Triples
• Arithmetic functions
• Euler's function & inversion formula
• Congruences
• The Chinese Remainder Theorem
• Recursive solution of polynomial equations modulo prime powers
• Cryptography & the RSA Algorithm
• Primitive roots, indices & Fermat's little theorem
• Quadratic Residues & quadratic reciprocity law
• Computations with Legendre & Jacobi symbols

• Sample space & Events
• Axiomatic foundation of Probability
• Classical Probability
• Conditional Probability
• Stochastic independence
• Random Variables & distribution functions
• Discrete & continuous Random Variables
• Distribution functions, moments, mean value & variance of a Random Variable
• Chebyshev's inequality
• Univariate discrete distributions: Bernoulli, Binomial, Poisson, Geometric & Pascal distributions.
• Univariate continuous distributions: continuous Uniform, Exponential, Gamma, Beta & Normal distributions.
• Bivariate random variables & distribution functions: Discrete & Continuous
• Conditional probabilities & independent random variables
• Generating functions of probabilities & moments.
• Law of Large Numbers
• Central Limit Theorem & Applications

• Games in extensive form:
  - tree representation 
  - information sets 
  - strategy & strategic equilibrium 
  - solution by backwards induction
• Games in normal form:
  - the mixed extension of a game
  - normal form & transformations
  - Nash's Theorem
• Matrix Games:
  - pure & mixed strategies 
  - Minimax Theorem 
  - solution via Linear Programming 
  - strategy domination 
  - symmetric matrix games 
  - equalizing strategies 
  - games against nature 
• Bi-matrix games
• Cooperative Game Theory
• Von-Neumann characteristic function
• 0-1 normalization
• Essential games & essential coalitions
• Shapley Value

• Sets, Relations & Functions
• Propositional Calculus & Mathematical Logic
• Natural Numbers: Peano axioms, Induction, well-ordering principle
• Real Numbers: Cardinality, countable & uncountable sets
• Complex numbers, polynomials & Gauss elimination

• Linear Algebra
• Matrices & Determinants
• Systems of Linear Equations
• Gauss-Jordan elimination methods
• Differentiation of real, multi-variable and vector functions
• Optimization of multi-variable functions
• Definite & Indefinite Integrals
• Integration techniques
• Differential Equations
• Mathematical Applications to Economics and to Business related problems

• Types of data
• Sampling techniques
• Presentation of statistical data
• Mean & Variance
• Introduction to Probability (sample space, events, properties of probabilities etc.)
• Discrete & continuous random variables
• Probability Distributions: binomial, Poisson & Normal distributions
• Confidence interval for the mean (when variance is known or unknown)
• Confidence interval for proportions
• Confidence interval for the difference of two means
• Confidence interval for the difference of two proportions
• Hypothesis testing for the mean value of a normal population,
  when the variance is known (Z-test) or unknown (t-test)
• Hypothesis testing for proportions
• Hypothesis testing for the difference of two mean values
• Hypothesis testing for the difference of two proportions
• Hypothesis testing for the ratio of two variances (F-test)
• Simple Linear Regression & Correlation: 
  - correlation coefficient
  - significance testing for the correlation & regression coefficients
  - method of least squares
  - prediction

• Linear Programming
• Simplex Method
• Duality Theory
• Optimality equations for finite & infinite horizon problems
• Network flow problems
• Inventory management, maintenance & replacement of equipment

• Programming in MATLAB
• Basic concepts of algorithms & programming
• Variables, Expressions, Input & Output
• Commands of control & repetition
• Functions
• Recursion
• Matrices
• Basic data structures
• Searching, Ordering
• Computational representation of numbers
• Mathematical applications
• Simulation & modeling
• Introduction to LATEX

• Algorithm notion:
  - run-time computation 
  - proof of correctness
  - recurrences
  - average-case performance
  - worst-case performance
• Algorithmic design methods:
  - divide & conquer
  - greedy algorithms
  - dynamic programming.
• Graphs & graph algorithms:
  - representation of graphs
  - minimum-cost spanning trees
  - shortest paths
• Algorithms for network problems: 
  - network flows
  - augmenting paths
  - matchings in bipartite graphs 
  - minimum-cost flows
• Approximation algorithms & Heuristics

• First order differential equations: 
  Linear, Bernoulli, Riccati, equations with separable variables,
  homogeneous & exact equations, Euler's multipliers.
• Existence, uniqueness & continuation of solutions
• Well-posed problems
• Second order linear differential equations:
  homogeneous & non-homogeneous differential equations
• Sturm's separation & comparison Theorems
• Power series solutions
• Systems of 1st order linear differential equations:
  homogeneous & non-homogeneous systems
• Sturm-Liouville boundary value problems
• Laplace Transformation
• Qualitative theory of ordinary differential equations