Zero Science Courses

• Introduce methodology and reflection into the mathematics learning process.
• To prepare students for the methodological and finalistic changes in Mathematics and/or Physics classes: use of symbolic language, fundamental and abstract concepts, and logical and structured deductive processes.
• Provide support material for the development of the first university course.

Credits: 2 ECTS = 20 hours.

Timing: From September 1st to 5th.

Schedule: from 9:00 to 13:30.

Mode: In-person group, rest streaming. It is recommended to do so in person, as some activities are only available in person.

Place: Faculty of Sciences. Mathematics Section: Classroom 3 (Mathematics Degree)

Registration: New students will be sent a message with registration instructions.

Contents:

• Block 1: Mathematical language and symbology
  Preliminaries. Sets and Relations. Symbolic Logic and Quantifiers. Direct and Indirect Proofs. Existence and Proofs by Contradiction. Proofs and Refutation.
• Block 2: Mathematical reasoning
  Induction. Introduction to geometry. Functions.

Certification: Only one qualification is considered PASSED=COURSE PASSED which are obtained when the following two conditions are met:

1. 90% of the questionnaires have been completed.
2. At least 75% of the questionnaires completed have been passed.

A certificate will be issued if you are PASSED.

Goals:

• Provide adapted, organized, and targeted material for new students.
• To offer, throughout the academic year, a study and learning platform that complements or corrects possible deficiencies in necessary knowledge, and that can be reviewed when detected and required.

This course is aimed at new students who have identified deficiencies in the 2nd year Baccalaureate curriculum. As a guide, we recommend taking the course if you fall into any of the following categories:

• You have obtained a score lower than 7 in the subject Mathematics II in the PAU or 2nd year of Baccalaureate.
• You have left unstudied some sections of the syllabus for the subject Mathematics II.
• Clearly identify that you have deficiencies in the management of the subject of mathematics.

Timing: Throughout the academic year (available from July 25, 2025).

Mode: Online

Registration: New students will be sent a message with registration instructions.

Organization and contentsThis course is completely voluntary and free of charge. It is offered online and has no time limit, but we recommend completing it before the official start of classes for the 2025-26 academic year.

It has a modular structure and can be completed sequentially (module by module in order, which is what we recommend) or selectively (only the modules of interest, for those who wish to address a specific knowledge gap).
The course contents are organized into 5 Blocks:

• Block 1: Numbers and operations
  Numbers, exponents, radicals, and scientific notation. Algebraic expressions, notable identities, and equations.
• Block 2: Geometry
  Plane figures. Solid bodies. Surfaces and volumes. Trigonometry. Vectors, lines, and planes in the plane and in space.
• Block 3: Algebra
  Matrices and systems of linear equations. Matrix algebra. Inverses of matrices and matrix equations. Determinants. Cramer's rule
• Block 4: Functions. Differential Calculus
  Basic functions. Elementary transformations. Rate of change. Limits. Derivatives. Applications
• Block 5: Integral Calculus
  Indefinite Integration: Primitives. Indefinite Integral. Immediate Integrals. Integration by Substitution. Integration by Parts. Integrals of Rational Functions.

You can access each block in any order you wish, but in each block you will have to complete a series of questionnaires.

Methodology: Each block consists of the following teaching materials:

• PDF Notes: Very visual, very graphic, with definitions, properties, examples and exercises.
• Videos explaining the material in the notes.
• Videos with typical problem solving.
• Sheets of proposed problems.
• Progress quizzes: As you achieve the minimum score on your attempts, you'll be able to access subsequent content.

Evaluation and certificationTo obtain the certificate of completion, students must complete at least 75% of the course questionnaires and obtain an average grade of at least 5 points. Once these requirements are met, a 3-credit certificate of completion will be issued.

Credits: 3 ECTS

Communication: The course has a Forum where you can ask questions about the course.
For any questions or individual inquiries regarding course organization, please contact the course coordinator at: cursoceromat@ull.edu.is