# Mathematical logic course training plan

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This is an illustrated basic course in mathematical logic. We invite everyone who wants to be creative in mathematics and programming. Enrol now and get started!

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This course offers basic knowledge in mathematical logic. Upon completion of the course, students will have acquired fundamental knowledge that is valuable in itself and will serve as the foundation for other studies. For example, software engineers strongly rely on logic-mathematical theories in their work.

No need to reinvent the wheel. The language of mathematical logic offers a great opportunity to practice this translation between languages and is used as a powerful formalised tool for transmission of information between distant languages. Most of the course content will be understandable for students with only a high school level of education. Some minor sections of the course will require knowledge of imperative programming and elements of mathematical analysis.

Goals, objectives, methods. Relation between mathematics and mathematical logic. Examples of logical errors, sophisms and paradoxes. Brief history of mathematical logic, discussing how problems mathematical logic faced and solved in its development, and how mathematical logic integrates further and further into programming.

The language of propositional logic has limited tools, so we talk about more complex languages based on predicate logic. The language of predicate logic offers tools for full and exact description of any formal notions and statements.

The axiomatic method makes it possible to solve many logical problems, errors and paradoxes. It is widely used in today's mathematics and the knowledge of it is vital for anyone using functional and logical programming languages. To learn about the possibilities of the algorithmic approach and the limitations of calculations, one must know the rigorous definition of algorithms and computability.

The module offers these definitions and defines algorithmically unsolvable problems. The module introduces the concept of algorithm complexity, which is an important factor when selecting algorithms to solve problems. The module also compares problems by complexity - this knowledge makes it possible to use any search algorithm to solve problem instead of search for the good algorithm.

Valentin M. Candidate of Physics and Mathematics, Senior Researcher. Author of 99 scientific, academic and teaching publications.

Author of 10 Academic Methodological Association-approved and one Ministry of Education-approved teaching aids imperative, logical and functional programming, mathematical logic and algorithm theory, computer algebra. Further education teaching for university teachers of mathematics.

Academic interests: mathematical logic, algorithm theory, functional programming, computer algebra, experimental mathematics, theory of numbers. Language proficiency: Intermediate level of English. Personal interests: traveling, literature, psychology, philosophy.

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Nadezhda Yu. Her academic interests include mathematical modeling, numerical methods and complexes of programs, models and methods for artificial intelligence, and programming.

### Mathematical Logic and Algorithms Theory

We use cookies, to provide social media features and to analyse our traffic. The goals of mathematical logic are: To provide a formal language for mathematical statements that is easily translatable into the natural language and that allows compact and convenient notation. To offer clear and unambiguous interpretation of such statements that is at the same time simple and close to the natural mathematical concepts.

We made sure to make this course informative and interesting for everyone! What will I learn? What do I need to know? Course Structure The course consists of 7 chapters: Chapter 1 - Mission of mathematical logic: Goals, objectives, methods.Specializations and courses in math and logic teach sound approaches to solving quantifiable and abstract problems. You'll tackle logic puzzles, develop computational skills, build your ability to represent real-world phenomena abstractly, and strengthen your reasoning capabilities.

The study of mathematics and logic as a discipline adds up to a lot more than what you learned in high school algebra. According to the Oxford Dictionary, math is "the abstract science of number, quantity, and space.

The study of math and logic combines the abstract science of numbers with quantitative reasoning that is fundamental in solving concrete problems.

For instance, engineers rely on geometry, calculus, physics, and other mathematical tools to ensure buildings are constructed safely. Computer programmers who create the mapping apps we use to navigate our cities apply problem-solving logic, algorithms, data, and probability to recommend the best route to take at a given time of day.

And even "soft science" disciplines like sociology rely on sophisticated statistical regression techniques to draw out insights about the workings of our human world. Thus, math and logic is important to us all in our daily lives, whether we use it directly in our own work or simply live in the modern world that it makes possible.

If you have great math skills and a deep passion for mathematics in its purest, most abstract form, the answer to this question is obvious: you can become a mathematician. However, you don't have to become a mathematician to use math and logic skills in your career. Virtually all jobs in computer science rely heavily on these skills, since programming is fundamentally about the creation of systems of logic and application of algorithms.

So whether you want to go into software development, data science, or artificial intelligence, you'll need a strong background in logic and discrete math as well as statistics. Math skills are becoming increasingly important for other jobs in both the hard and soft sciences as well.

This is due in part to growing opportunities to leverage computer science approaches, particularly data science, to answer pressing questions with findings from larger datasets than ever before.

For example, skills in statistical analysis are increasingly central to the work of natural scientists looking for patterns in the growth of certain species populations -- or for epidemiologists studying the spread of public health threats.

Online courses are a popular way to learn about many different topics in computer science, and this format also lends itself well to building your math and logic skills.

In fact, many students use online courses to fulfill mathematics prerequisites for advanced computer science degrees. As with computer science and other areas of study, taking courses online gives you a flexible option to develop the skills you need while continuing to work, study, or raise a family.

Online versions of courses are also often significantly less expensive than on-campus counterparts, even in cases where the course material is identical. Coursera offers a wide range of courses in math and logic, all of which are delivered by instructors at top-quality institutions such as Stanford University and Imperial College London.

You can find courses that fit your specific career goals, whether that's broad skills in logicproblem solvingor mathematical thinkingor more specialized areas like mathematics for machine learning or actuarial science. Coursera also offers short Guided Projects to help you practice and hone your math skills.

Explore Math and Logic. Math and Logic Outlined Info Action.

## We help parents become great mentors and students become great thinkers.

Filter by:. Earn Your Degree. Most Popular Certificates in Math and Logic. Introduction to Discrete Mathematics for Computer Science.

Specialization 5 Courses. Cryptography I. Game Theory. Mathematics for Machine Learning: Linear Algebra. Imperial College London. Mathematics for Machine Learning. Specialization 3 Courses. Johns Hopkins University. University of Michigan.By carefully planning classroom experiences, one can help children develop logic and reasoning skills that they can use to make sense of their world. Three-year-old Scott insists that his tall pile of blocks contains more than Rochelle's flat train of blocks, even after his teacher helps him count each group.

Scott is still using observation to tell him that his "big" pile has more. It will take more such teacher-- assisted experiences and a developmental leap for Scott to realize that his initial perception was incorrect.

Preschoolers at the preoperational stage of development use their perceptions of the environment, along with bits of information gathered during their past experiences, to understand their world.

They base their understanding on what they see rather than on logic. They need to go through many illogical thinking processes before they can even begin to make logical sense of their world.

### Math and Logic

In providing your children with opportunities to learn through play, bear in mind the following characteristics of their thinking:. Judging by appearances. When the form or appearance of a material changes, it's difficult for preschoolers to understand that quantities remain the same or are "conserved". For instance, during snack time, Janelle dumps her box of animal crackers on the table. Latisa looks into her own tightly filled box of crackers, then pouts and asks why Janelle has more crackers.

She doesn't logically understand that if Janelle's crackers were placed back in the box, the quantities would look and be the same. Looking at one thing at a time.

Because it's hard for preschoolers to focus on more than their own singular perception, they tend to sort objects by one characteristic, rather than by two. If given some small blocks of different sizes, colors, and shapes, for example, young threes might decide to sort them by lining them up by size and calling them a "parade. Not knowing numbers. Preschoolers are also quite illogical when it comes to number concepts.

As Charlie pours buckets of water and recites by rote, "four, five, six," his counting may not correspond at all to the amounts he is pouring. Again, it's through concrete experiences that he will come to understand the meaning of numbers and counting. Allow for different learning styles.

Some children like to jump right in and mess around. Provide these children with lots of open-ended materials to explore.

Other children are more comfortable watching an activity and asking questions. Make sure there's plenty of time for them to discuss what's happening. Stimulate children's curiosity and thinking skills. Offer a range of intriguing manipulatives. For example, ask children to compare colored rods by size and string beads to create patterns. Point out cause-and-effect relationships.This course is an introduction to Logic from a computational perspective.

It shows how to encode information in the form of logical sentences; it shows how to reason with information in this form; and it provides an overview of logic technology and its applications - in mathematics, science, engineering, business, law, and so forth.

This course was so helpful. I think I now understand the fundamentals of mathematical logic. I truly recommend this course to anyone who is interested in studying logic! Somehow difficult in the last several weeks. As almost all the materials are all in words, students may sometimes feel bored seeing all lines and complex tables. Very interesting course But some parts are not just to technical but rather for technicians and not for persons looking more into the theoretical aspects.

I feel like some things could have been explained better, maybe a better description of how the fitch tool worked. Other than that, it was a great course! Access to lectures and assignments depends on your type of enrollment.

If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:. When you purchase a Certificate you get access to all course materials, including graded assignments.

Learn more. More questions? Visit the Learner Help Center. Math and Logic. Introduction to Logic. Offered By.

## Ages & Stages: Helping Children Develop Logic & Reasoning Skills

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For more information, please see our University Websites Privacy Notice. The Graduate Certificate in Logic provides students in linguistics, mathematics, philosophy, and related areas such as cognitive science and computer science with a comprehensive training in logic and formal methods, for use in their future careers in both academia and industry. The program is interdisciplinary by design, with enrolled students taking courses in multiple departments, and attending the bi-weekly inter-departmental Logic Colloquium.

Students have access to the full offering of logic courses and seminars offered each semester by the faculty of the UConn Logic Groupand all are encouraged to participate in the numerous special activities the Logic Group organizes, such as the Annual Logic Lectureand the various logic conferences hosted in Storrs each year. The certificate facilitates advanced studies in a variety of topics, including: mathematical logic; the theory of computation; formal semantics; natural-language reasoning; vagueness, probability, and contradiction; and the application of logic and formal methods to law and cognitive science.

Administered through the UConn Logic Group, which is an internationally recognized center of logic research excellence, the certificate will provide students with a broad and comprehensive background in the subject, with a specific focus on interdisciplinary applications.

Anyone enrolled in, or accepted into, a graduate degree program at UConn is eligible to apply for admission to the certificate program as an additional qualification, provided they will not have received their degree prior to the start of the certificate program. All students enrolled in the certificate program are expected to be active members of the UConn Logic Group. Required Course: All students are required to take a 1-credit, one-semester independent study with a Certificate Directorwhich includes participation in the Logic Colloquium.

Elective Courses: Four courses from among our Group's regular course offerings. Courses not listed above may be substituted on a case-by-case basis by approval of Certificate Directors.

Timing: A student must complete all requirements for the certificate within three years of initial enrollment. All applicants enrolled in a graduate program at UConn at the time of application are eligible to have their application fee waived. Please email the Graduate School to obtain a waiver prior to completing your application.

Apply today! For additional information about the program, or if you have any questions about your application, please contact the Certificate Directors. Introduction The Graduate Certificate in Logic provides students in linguistics, mathematics, philosophy, and related areas such as cognitive science and computer science with a comprehensive training in logic and formal methods, for use in their future careers in both academia and industry.

Objectives Logic is a multifaceted subject that connects many disciplines. Eligibility Anyone enrolled in, or accepted into, a graduate degree program at UConn is eligible to apply for admission to the certificate program as an additional qualification, provided they will not have received their degree prior to the start of the certificate program.Homeschool Supermom. Want to know a bit more about the Discovery Method and Math Inspirations?

K-8 Math Curriculum. See Inside. Parent Training. See How It Works. Learn More. Families around the world thrive with Math Inspirations Meet a few of our customers and hear how Math Inspirations has impacted their lives.

You can quote me on that. I keep telling people about it even though I am not finished with the course yet. Read More Testimonials. Discover how Math Inspirations can help your homeschool math program:. Get Your Free Starter Kit. Discovery Method K-8 Curriculum Powerful, student-led curriculum focused on logic and problem solving that is designed specifically for the special parent-mentor relationship found in homeschooling. Grow your students into powerful, confident thinkers with Math Inspirations.

Get In Touch. Request A Free Consultation. Get Started. Find out how homeschool families across the world are thriving.Meetings Tues. It is not strictly required, though it is recommended, and covers a large portion of the course material.

Also on reserve are Mathematical Logic by Ebbinghaus, Flum, and Thomas, and A Concise Introduction to Mathematical Logic by Rautenberg, which you may find helpful as references, especially near the beginning of the term.

Additional supplemental references will be provided throughout the course. This course will provide a graduate-level introduction to mathematical logic, with a strong focus on several mathematical applications.

No prior knowledge of mathematical logic is assumed, but some mathematical sophistication and knowledge of abstract algebra will be helpful.

As the course progresses, please consider which topic you'd like to investigate further it could be some mathematical application or a basic theorem we won't coverand meet with me by April 8 to discuss it and for advice on helpful sources.

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Presentations will occur the during the final 5 classes; the report will be due on May Homework: You should hand in solutions to most of the problems, though you are not required to work on every single one.

You are encouraged to work together on solving them if you'd likethough please write up the solutions yourself and indicate the collaborators. I strongly recommend that you look carefully at each such problem, and at least attempt a solution. Problems are Exercises from Hinman's text, unless otherwise indicated. Class Schedule tentative : Chapters are from Hinman's text. Supplementary material will be indicated throughout the term. Tues Feb 2: First class: Introduction to 4 main topics; survey of applications Thurs Feb 4: First-order logic: syntax and semantics Ch.

Tues Mar 2: Proof of compactness theorem Ch.