To train mathematicians specialized in analyzing, designing, and creating algorithmic solutions to complex problems, to respond, with a high sense of ethics, innovation, and business intelligence, to the needs of a changing society.
The graduate of the Bachelor's Degree in Algorithmic Mathematics will be able to design, implement and implement algorithms adaptable to the dizzying changes of society, from the formal understanding and comprehensive application of mathematical modeling, computation, mathematical foundations, and algorithmic, to generate predictions, classifications, abstractions, estimations and error margin reductions applicable to complex problems in areas such as financial asset trading, information security, risk analysis of volatile systems, security and public health, among others. Likewise, he/she will be able to work in interdisciplinary teams, with a high sense of ethics and business intelligence.
KNOWLEDGE
- Real numbers.
- Functions: Limit and Continuity.
- The Derivative.
- The Integral.
- Preliminaries (sets, functions, induction, equivalence, and partitions).
- Combinatorial calculus (sorting, permutations, combinations, inclusion-exclusion principle).
- Integers and divisibility.
- Real and complex numbers.
- Polynomials and equations.
- Algorithms and Control Structures.
- Functions and Libraries.
- Data Structures.
- Sorting and Searching Algorithms.
- Strategies for training mathematical thinking.
- Learning unit integration activities.
- Propositional calculus and methods of proof - Plane Geometry.
- Space Geometry.
- Analytic Geometry.
- Applications of the integral.
- Indeterminate forms.
- Successions and series
- Vector functions (normal vector, tangent vector, length, etc.).
- Vector spaces.
- Linear Transformations (Matrices).
- Determinants.
- Vectors and eigenvalues of matrices.
- Inner product spaces.
- Methodologies for solving and approaching mathematical problems.
- Exposure to real problems and solutions.
- Proactivity in the integration of learning units.
- Solution with computational tools (programming, R, Python, MATLAB).
- Probability axioms.
- Independence and conditional probability.
- Computational probability and simulation.
- Bernoulli tests, associated distributions, and limit theorems.
- Continuous probability distributions.
- Functions of several variables (gradient, rotational).
- Applications of the calculus of several variables.
- Surface integrals.
- Multiple integrals.
- Line integrals.
- Cayley-Hamilton theorem.
- Bilinear forms (inner product and quadratic).
- Diagonalization.
- Pseudoinverses.
- Matrix decomposition.
- Basis (graphs, paths and cycles, trees, bipartite graphs, Eulerian paths).
- Pairing.
- Connectivity.
- Planar graphs.
- Coloring.
- Mathematical statistics.
- Parametric statistical inference.
- Bayesian statistics.
- Computational statistics.
- Sets.
- Relationships, Functions, and Orders.
- Numerical Systems Construction.
- Cardinality.
- Fundamentals of Entrepreneurship.
- Fundamentals of non-verbal language.
- Characteristics, Elements, and Qualities of Oral and Written Communication.
- Academic writing.
- Fundamentals of effective communication.
- Neurolinguistic Programming.
- Digital communication.
- The VICA environment.
- Complexity in the Anthropocene.
- Heuristics and problem solving.
- Problem-solving process and models.
- Fundamentals of data analysis for decision making.
- Relationship between data analysis and interpretation and decision making.
- Business intelligence.
- Steps to make a decision.
- Types of decisions.
- Certainty, Uncertainty, and Risk.
- Quantitative criteria.
- Challenges of the contemporary world.
- The phenomenon of globalization.
- Ethics and politics.
- Regulatory framework of Algorithmic Mathematics.
- Lambda Calculus.
- Functional Languages.
- Memory management.
- Modules and data abstraction.
- Object-oriented languages.
- Parallel and distributed systems.
- Analysis (Generalities, master theorem).
- Algorithms (Greedy Algorithms, Divide and Conquer, String Algorithms).
- Dynamic programming.
- Randomized algorithms.
- Complexity theory (complexity classes, reductions, and approximation algorithms).
- Basic topology.
- Limits and continuity.
- Derivation.
- Successions of functions.
- Elements of complex analysis.
- Finite Automata and regular expressions (DFAs, NFAs, PDAs).
- Stack automata and context-free languages.
- Turing machines and recursively enumerable languages.
- Complexity Classes (P, NP, Exp).
- Notions of numerical analysis (error, convergence, well-posed problems, stability).
- -Numerical solutions of linear systems and matrix inversion.
- Iterative solutions of nonlinear equations.
- Numerical integration.
- Numerical solution of ordinary differential equations.
- Ordinary Differential Equations (Laplace).
- Elements of dynamic systems.
- Introduction to Partial Differential Equations.
- Methods of Solution of Differential Equations (Z-Transform).
- Random walks.
- Markov Chains.
- Random graphs.
- Poisson processes.
- Brownian motion.
- Measurement.
- Integral.
- Spaces of integrable functions.
- Radon-Nikodym Theorem and conditional expectation.
- Limit theorems in probability.
- Simple and multilayer perceptron.
- Backpropagation (gradient descent).
- The Hopfield model.
- Kohonen networks.
- Genetic algorithms.
- Linear models.
- Elements Generalized linear models.
- Time series.
- Linear Programming.
- Notions of Integer Programming.
- Elements of Convex Programming.
- Applications (short paths, flow in networks, maximum matching).
- Bayesian estimation.
- Stochastic difference equations.
- Kalman filter.
- Discrete stochastic control (closed loop, open loop).
- Smoothing.
- Clusters.
- Rings.
- Fields.
- Financial and trading terminology and backtesting.
- Technical and fundamental analysis.
- Portfolio and risk managemen.t
- Basic Mean Reversion Strategies.
- Basic momentum strategies.
- Types of instruments and models.
- Portfolio and trading strategies.
- Arbitrage strategies.
- Cox-Ross-Rubinstein model.
- Futures.
- European options (Black-Scholes, Ito's Lemma).
- Downtime.
- American options.
KNOW-HOW
- Functions: Limit and Continuity.
- The Derivative.
- The Integral.
- Preliminaries (induction and partitions).
- Combinatorial calculus (ordering, permutations, combinations).
- Polynomials and equations.
- Algorithms and Control Structures.
- Functions and Libraries.
- Data Structures.
- Sorting and Searching Algorithms.
- Strategies for training mathematical thinking.
- Challenge Exposure.
- Learning unit integration activities.
- Solution with computational tools (calculators, cell phones, spreadsheets, latex).
- Propositional calculus and methods of proof.
- Analytical Geometry.
- Applications of the integral.
- Indeterminate forms.
- Successions and series.
- Vector functions (normal vector, tangent vector, length, etc.).
- Vector spaces.
- Linear Transformations (Matrices).
- Determinants.
- Vectors and eigenvalues of matrices.
- Inner product spaces.
- Methodologies for solving and posing mathematical problems.
- Exposure to real problems and solutions.
- Proactivity in the integration of learning units.
- Solution with computational tools (programming, R, Python, MATLAB).
- Computational probability and simulation.
- Bernoulli tests, associated distributions, and limit theorems.
- Continuous probability distributions.
- Applications of multivariate calculus.
- Surface integrals.
- Multiple integrals.
- Line integrals.
- Bilinear forms (inner product and quadratic).
- Diagonalization.
- Pseudoinverses.
- Matrix decomposition.
- Basis (graphs, paths and cycles, trees, bipartite graphs, Eulerian paths).
- Pairing.
- Connectivity.
- Planar graphs.
- Coloring.
- Mathematical statistics.
- Parametric statistical inference.
- Bayesian statistics.
- Computational statistics.
- Numerical systems construction.
- Design thinking for innovation.
- Validation of business initiatives.
- Financing and profitability.
- Smart growth of private companies.
- Technology development management.
- Oral and Written Presentation Strategies and Techniques.
- Academic text composition and technical-scientific writing.
- Coaching.
- Effective communication strategies.
- Accessing and processing information through ICTs.
- Abstraction, brainstorming, analogy, decomposition into components, hypothesis testing, focusing, and lateral thinking.
- Need and definition of the problem. Search and selection of solutions. Implementation and control.
- Cause and effect analysis.
- GROW Model.
- OODA Model.
- PDCA model.
- Preparation of data for analysis.
- Data analysis methodologies are most suitable for different types of studies.
- Application of data analysis in strategic planning.
- PART MODEL. Decision tree. Qualitative criteria. Brainstorming. Synectics.
- Decisions by consensus. Delphi technique. Fishbowl. Didactic interaction.
- Rational and negotiated decisions.
- Philosophical analysis of ethical development.
- The ethical response to contemporary challenges.
- Functional Languages.
- Memory management.
- Object-oriented languages.
- Parallel and distributed systems.
- Analysis (Generalities, master theorem).
- Algorithms (Greedy Algorithms, Divide and Conquer, String Algorithms).
- Dynamic programming.
- Randomized algorithms.
- Limits and continuity.
- Derivation.
- Successions of functions.
- Elements of complex analysis.
- Finite automata and regular expressions (DFAs, NFAs, PDAs).
- Stack automata and context-free languages.
- Turing machines and recursively numerical languages.
- Numerical solutions of linear systems and matrix inversion.
- Iterative solutions of nonlinear equations.
- Numerical integration.
- Numerical solution of ordinary differential equations.
- Ordinary differential equations (Laplace).
- Elements of dynamic systems.
- Introduction to partial differential equations.
- Methods of solution of equations in differences (Z-transform).
- Random walks.
- Markov chains.
- Random graphs.
- Poisson processes.
- Brownian motion.
- Integral.
- Radon-Nikodym theorem and conditional expectation.
- Limit theorems in probability.
- Simple and multilayer perceptron.
- Backpropagation (gradient descent).
- The Hopfield model.
- Kohonen networks.
- Genetic algorithms.
- Linear models.
- Generalized linear model elements.
- Time series.
- Linear programming.
- Notions of integer programming.
- Elements of convex programming.
- Applications (short paths, network flow, maximum matching).
- Bayesian estimation.
- Stochastic difference equations.
- Kalman filter.
- Discrete stochastic control (closed loop, open loop).
- Smoothing.
- Portfolio and risk management.
- Basic mean reversion strategies.
- Basic strategies for the moment.
- Portfolios and trading strategies.
- Arbitrage strategies.
- Cox-Ross-Rubinstein model.
- Futures.
- European options (Black-Scholes, Ito's Lemma).
- Stopping times.
- American options.
KNOWING HOW TO BE AND LIVE TOGETHER
- Collaborative work
- Assertive communication
- Interdisciplinarity
- Professional ethics
- Responsibility
- Professionalism
- Honesty
- Resilience
- Sustainable thinking
- Social Responsibility
Graduates of the Algorithmic Mathematics program will be able to work professionally in different sectors of society, carrying out activities related to algorithmic problem-solving in areas such as related to algorithmic problem-solving in areas such as algorithmic trading, data analysis, business intelligence, genomics, finance, economics, and teaching, among others.
Towards the end of their studies, they will be guided towards the branch of their interest among which Algorithmic Trading will have particular relevance and will be mandatory for the formative contributions of this career.
Algorithmic Trading
- It is an area that is currently developing in a vertiginous way all over the world. The vision of auction floors full of stockbrokers competing to win the purchase and sale offers before the different market agents are something that is definitely in the past. Today, market operations are recorded on computers, from the bids that are entered in the order books to the allotment of instruments. Nowadays, financial operators must have computer training and the possessing advanced mathematical knowledge gives them an important competitive advantage.
- It naturally requires mathematicians due to the dynamic variation in the structure of markets. Engineers are trained to build by identifying more or less static patterns and generally controlled variables that determine how they build their structures, and they are uniquely suited to make use of these specific methodologies. For example, civil engineers are taught construction techniques that depend on soil conditions, environment, climate, geographical location, seismicity, etc. Once the global pattern is identified, the best construction technique is chosen and the structure is designed. This is more or less the case in all areas of engineering. Markets on the other hand have a dynamically varying structure and it is on that structure that we have to build. You need the ability to develop methods that adapt to market conditions. There is no one best method, everything evolves continuously and therefore mathematical talent is required to determine when a good method is no longer good and also to adapt to new conditions or even to decide that for the moment there is too much turbulence and it is not good to participate.
- Many tools are needed such as time series analysis, control theory, Kalman filter, probability, estimation theory, statistics, data science, game theory, machine learning, operations research, etc... Each of these areas must be studied in depth and formally. And this is a great advantage. If we forget Algorithmic Trading we will have training equivalent to that of many other similar programs equivalent to that of many other similar programs and our graduates will also be able to work there to reinforce those labor niches that, as presented in this document, have been growing rapidly for some time now.
the document has been growing rapidly for some years now.
- It will be precisely the common thread that will allow us to link mathematical concepts with a vast source of real problems related to the analysis of markets and the time series they generate. At the same time that students develop their subjects, they will participate in workshops in which they will put into practice what they have learned, building and testing their strategies. This will gradually introduce them to financial circles until they are trading on their own.
- It opens a new range of job opportunities for graduates of an academic program in the area of Mathematics. Traditionally, their destination has been almost exclusively teaching. But nowadays this is totally out of perspective because even graduates of master's and doctoral academic programs in mathematics find it very difficult to find job programs mathematics find it very difficult to find opportunities in academia.
With this new profile, our graduates could form investment funds to manage and build their own companies. Using the facilities provided by technology, from modest facilities that may be centralized in their own homes, they will be able to maintain investment accounts in the financial markets of their choice in the world and hire servers close to the physical sites where the computer infrastructure is located to carry out market operations. This will open up opportunities for mathematicians that have never been seen before in Mexico.
- It favors the integration of the work of mathematicians with engineers. Many tasks require the skills of engineers in computer science, networks, data science, etc. For example, interconnection systems with financial centers have to be programmed by experts in telecommunications and computing. The processes known as backtesting, which consist of testing investment strategies with historical data and collecting and evaluating statistical information, could be performed by data science engineers. Databases to keep track of operations for accounting, fiscal and administrative purposes would be the domain of computer engineers, so we could continue to list collaborations between mathematicians and engineers. This means that in the professional development of our specialists in Algorithmic Mathematics many other areas that are cultivated in the IPN itself would benefit greatly.
In Mexico, we were not able to locate studies that reveal possible companies that hire professionals with the profile of a career in Algorithmic Mathematics. However, for the U. S. A. we found the document "Careers in Applied Mathematics" produced by the Society for Applied Mathematics (SIAM).
In this reference, we present the following list of mathematics-related job titles that have appeared on U. S. A. job vacancy pages that relate to mathematics. From it we filtered those suitable for graduates of the career we propose: Analyst, Consultant Analyst, Administrator Analyst, Applied Mathematician, Researcher, Biostatistics Specialist, Business Analyst, Business Intelligence Developer, Data Analyst, Data Processing Specialist, Data Scientist, Forecasting Analyst, Functional Analyst, Mathematician, Video Game Designer, Operations Researcher, Geolocation Specialist, Pricing Specialist, Computer Scientist, Information Analyst, Quant Analyst, Functional Analyst, Mathematician Video Game Designer, Geolocation Specialist, Pricing Analyst, Computer Scientist, Information Analyst, Quant, Mathematician, Modeler, Operations Researcher, Operations Support Specialist, Operations Support
Operations Support Specialist, Planning Strategist, Product Manager, Programmer, Project Manager, Quality Control Specialist, Quantitative Analyst, Quantitative Developer, Quantitative Scientist, Risk Analyst, Simulation Specialist, Statistics Specialist, Supply Chain Strategist, and Analyst.
Organizations offering these jobs include:
- Academic and research institutions.
- Aerospace companies.
- Central banks.
- Organizations engaged in forecasting (weather, financial, etc.).
- Chemical and pharmaceutical manufacturing companies.
- Communications service providers.
- Information services and software development companies.
- Energy Systems development firms.
- Electronic component and computer manufacturers.
- Engineering research organizations.
- Engineering research organizations.
- Financial services and investment management companies.
- Governmental laboratories, research and development offices.
- Financial services and investment management firms.
- Government laboratories, and research offices.
- Insurance companies.
- Health care-related companies.
- Petroleum and petroleum products producers.
