Penn State Undergraduate Admissions Penn State University

4-Year Baccalaureate Majors

Majors by Area of Interest


ENGINEERING

Aerospace Engineering (Start at any Campus and Finish: University Park)

This major emphasizes the analysis, design, and operation of aircraft and spacecraft. Students learn the theories and practices in the fundamental subjects of aeronautics, astronautics, aerodynamics and fluid dynamics, aerospace materials and structures, dynamics and automatic control, aircraft stability and control and/or orbital and attitude dynamics and control, air-breathing and rocket propulsion, aircraft systems design and/or spacecraft systems design. The development and use of teamwork and communications skills for effective problem solving is stressed. Graduates in aerospace engineering find employment in government laboratories, large and small aerospace firms, and in nontraditional positions that also require the use of systems engineering approaches to problem solving; they can also pursue graduate study in aerospace engineering and related fields.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Architectural Engineering (Start at any Campus and Finish: University Park)

This major emphasizes the application of scientific and engineering principles to the planning, design, and construction of buildings and building systems. The goal of the program is to provide engineering graduates with the best education available for careers in the building professions. Graduates will have the ability to practice as registered professional engineers in a variety of areas, both public and private, related to the planning, design, construction, and operation of buildings and to assume a place of leadership in society. Four options are available in the ten-semester major: Construction, which emphasizes building construction engineering and construction management; Lighting/Electrical, which emphasizes the design of lighting and electrical systems for buildings; Mechanical, which emphasizes the design of heating, ventilating and air-conditioning systems in buildings; and Structural, which emphasizes the analysis and design of building structural systems.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Biological Engineering (Start at any Campus and Finish: University Park)

This major helps students prepare for careers involving the application of engineering principles to biological and agricultural production systems, processing systems, and conservation of land and water resources. Education in mathematics, physics, and engineering sciences common to all engineering disciplines is provided along with specialized training in biological and agricultural sciences. The curriculum covers agricultural and biological engineering, including food engineering, postharvest handling and processing of commodities, power and machinery development and applications, resource management and utilization, soil and water management structures and their environmental modifications, product synthesis using microbiological organisms, and food safety. A student can select the Agricultural Engineering option or the Biological and Food Engineering option.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Biomedical Engineering* (Start at any Campus and Finish: University Park)

The Biomedical engineering curriculum emphasizes the continuous integration of classical and modern engineering principles with the life sciences and health care. Bioengineers apply these skills to innovation in the health care industry, basic biological sciences, and the underpinning of medical practice. Graduates of the program are expected to assume positions in the health care industry, to pursue further studies of the biomedical and engineering sciences, or go on to study medicine.
(College of Engineering)

* Accredited by the Engineering Accreditation Commission of ABET, 111 Market Place, Suite 1050, Baltimore, MD 21202-4012; telephone, 410-347-7700; www.abet.org.

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Chemical Engineering (Start at any Campus and Finish: University Park)

Chemical engineers are employed in pharmaceutical and biotechnical companies, semiconductor manufacturing, start-up companies converting the latest laboratory discoveries to large-scale commercial production. Chemical engineers develop new ways to manufacture medicines and plastics; develop control systems that enable the safe production of products from semiconductors to household soap; design chemical and petroleum plants; research the effects of artificial organs on blood flow; and develop the equipment and processes necessary for advances in biotechnology. Chemical engineering emphasizes the practical application of chemistry for the development of new products and processes. This major provides students with fundamental skills in problem solving, analysis, and design, along with hands-on experience in practical applications. Students have numerous opportunities to pursue specialized areas, including formal options in Bioprocess and Biomolecular Engineering, Energy and Fuels, and Polymer Engineering.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Civil Engineering (Start at any Campus and Finish: Harrisburg)

The program in Civil and Environmental Engineering is designed to provide the basic undergraduate education required for private practice and public service in civil engineering, and/or graduate education. Emphasis is placed on the fundamentals of civil engineering principles and design techniques. Students utilize basic engineering science concepts in several of the different specialty areas (e.g., construction/management, environmental, materials/pavement design/geotechnical, structures, transportation, and water resources). Students choose an area of specialization for professional practice or graduate studies. Their area of specialization culminates in a capstone design experience.
(Capital College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Civil Engineering (Start at any Campus and Finish: University Park)

The program in Civil and Environmental Engineering is designed to provide the basic undergraduate education required for private practice and public service in civil engineering, and/or graduate education. Emphasis is placed on the fundamentals of civil engineering principles and design techniques. Students utilize basic engineering science concepts in several of the different specialty areas (e.g., construction/management, environmental, materials/pavement design/geotechnical, structures, transportation, and water resources). Students choose an area of specialization for professional practice or graduate studies. Their area of specialization culminates in a capstone design experience.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Computer Engineering (Start at any Campus and Finish: Behrend)

The mission of the faculty of the undergraduate Computer Engineering program is to provide students with the knowledge and experience needed to pursue a productive lifelong career in industry or to engage in further study at the graduate level. Students participate in a balanced program of instruction covering the basic principles of the design and application of computer systems. The program includes coverage in breadth and depth in basic science, engineering, and abstract concepts of information handling. Students will specialize in and be prepared for careers in the design, analysis, and use of hardware, software, and systems. The program is structured to ensure that graduates have a clear understanding of the design and applications of computers as well as the ability to apply this knowledge throughout their professional careers.
(College of Engineering)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Computer Engineering (Start at any Campus and Finish: University Park)

This major provides students with a strong foundation in computer engineering through a combination of classroom study, design projects, and laboratory experience. Analysis and design of computer hardware and software systems are stressed. Built upon a core of science and mathematics courses, this major has the objective of educating graduates to be problem solvers. Students acquire the ability to work as members of a team toward successful attainment of a common goal, preparing them for industry or further study in graduate school. In addition, written and oral communication skills are developed, culminating in a senior design project that stresses communication as well as engineering content.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Computer Science (Start at any Campus and Finish: Harrisburg)

This program is designed to help students prepare for employment as computer scientists in engineering, scientific, industrial, and business environments as software developers, programmers, and systems analysts. While most students will enter the job market directly upon graduation, graduate school in computer science or related areas is also an option. Selection of electives can be tailored for students pursuing this path. The Computer Science major provides a solid foundation in the areas of systems programming, algorithm design, artificial intelligence, and engineering large software systems using state-of-the-art methodologies and programming languages. Students may expect to: develop a solid foundation in mathematical studies relevant to computer science; master skills in computer science; enjoy possibilities for internships and part-time employment with local companies; and become problem solvers. These goals are consistent with the goals outlined by the Association of Computing Machinery.
(Capital College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Computer Science (Start at any Campus and Finish: Behrend)

This major builds on a firm foundation of computer science, mathematics, and natural science courses. The major stresses the fundamentals of computer science—programming, discrete math, data structures, graphics, analysis and design of algorithms— and their practical applications in system programming, database management, scientific visualization, and telecommunications. Graduates of this program will be prepared for a wide variety of computer-oriented careers in business, industry, and government, particularly in areas that require the practical application of computer science concepts and techniques to solving problems in the natural sciences. In addition, graduates will be prepared to pursue graduate study in computer science or in computationally intensive subdisciplines of the natural sciences, such as bioinformatics, computational biology, computational physics, or computational chemistry.
(The Behrend College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Computer Science (Start at any Campus and Finish: University Park)

Computer Science is concerned with the analysis, design, and applications of computing software and systems. It includes a core foundation in computer hardware and software with emphasis on the design of efficient, fault-free software. It includes programming languages, data structures, compilers, operating systems, databases, and artificial intelligence. The major is designed to provide fundamental training in preparing graduates for positions in schools, commerce, industry, and government. Students should consult their advisers in formulating suitable programs.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

This major is for students interested in the College of Earth and Mineral Sciences, but are undecided about which major they would like to select. Beginning studies with an "undecided" major allows students to explore the many different majors offered within this college and learn more about the specific disciplines that are available to them.

College of Earth & Mineral Sciences

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Electrical Engineering (Start at any Campus and Finish: Harrisburg)

The bachelor of science degree program in Electrical Engineering provides a solid background in electrical engineering sciences. It also provides an opportunity for students to pursue interests in electrical and electronic circuits, including digital circuits and VLSI and its fabrication, microprocessors and their applications, electromagnetics, communications, control systems, and digital image processing and computer vision. Through a senior capstone design project, the curriculum emphasizes written as well as verbal communication and teamwork approach among the students to attain a common goal. This program helps its graduates develop capabilities to analyze and design a variety of electrical and electronic systems found in many industrial and government settings as well as provide a foundation for further graduate studies.
(Capital College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Electrical Engineering (Start at any Campus and Finish: Behrend)

This major provides students with a strong foundation in electrical engineering through a combination of classroom study, projects, and laboratory experience. Analysis and design of electrical and computer systems are stressed. Built upon a core of science and mathematics courses, this major has the objective of educating graduates to be problem solvers. Students acquire the ability to work as members of a team toward successful attainment of a common goal, preparing them for work in industry or further study in graduate school. In addition, written and oral communication skills are developed, culminating in a senior design project that stresses communication as well as engineering content.
(The Behrend College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Electrical Engineering (Start at any Campus and Finish: University Park)

Electrical engineering is the application of electronics, electrical science and technology, and computer systems to the needs of society. The Electrical Engineering faculty is committed to providing a curriculum that educates students for professional careers in electrical engineering in diverse industries such as defense, communications, transportation, manufacturing, health care, construction, and entertainment. Graduates also go on to advanced study in electrical engineering or a related field. Students acquire a broad knowledge base in electrical circuits, digital systems, electronic devices, electromagnetics, and linear systems as well as expertise in one or more areas of specialization. Students learn electrical engineering theoretical, analytical, and design concepts through lecture-based courses. Additional problem-solving skills and practical experience are developed through design projects and laboratory assignments, which also provide opportunities for learning team building, teamwork, and technical communication skills.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Energy Engineering (Start at any Campus and Finish: University Park)

The Energy Engineering major is designed to address the growing impact and demand for energy in society and to equip students with the knowledge necessary to become valuable contributors in addressing society’s energy needs and demands. Along with basic engineering skills, the program integrates skill sets in the physical sciences (chemistry, engineering, mathematics, and physics) and social sciences (economics, policy, and management) to ensure successful career opportunities in advancing the technology and management of energy; innovators and entrepreneurs in the energy sector; and educators, practicing engineers, and national leaders in the energy and associated environmental health and safety, policy, and economic fields.
(College of Earth and Mineral Sciences)

College of Earth & Mineral Sciences

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

This major is for students interested in the Behrend College, School of Engineering, but are undecided about which major they would like to select. Beginning studies with an "undecided" major allows students to explore the many different majors offered within this college and learn more about the specific disciplines that are available to them.

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

This major is for students interested in the College of Engineering, but are undecided about which major they would like to select. Beginning studies with an "undecided" major allows students to explore the many different majors offered within this college and learn more about the specific disciplines that are available to them.

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Engineering Science* (Start at any Campus and Finish: University Park)

Engineering Science is a multidisciplinary honors program that emphasizes enhanced understanding and integrated application of engineering, scientific, and mathematical principles. The program provides a broad foundation in the sciences and associated mathematics that underlie engineering and provides students the opportunity to obtain a depth of knowledge in an area of their choice through technical electives and an honors thesis. The curriculum is designed for students who seek to link the engineering disciplines with science. Focus areas of study include, but are not limited to, electrical, mechanical, civil, bioengineering, and materials and are typically interdisciplinary. Engineering Science students achieve both depth and breadth in engineering and science, are able to function across disciplines, and graduate well prepared for advanced studies as well as professional employment.
(College of Engineering)

* Accredited by the Engineering Accreditation Commission of ABET, 111 Market Place, Suite 1050, Baltimore, MD 21202-4012; telephone, 410-347-7700; www.abet.org.

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Environmental Systems Engineering* (Start at any Campus and Finish: University Park)

Environmental Systems Engineering is an interdisciplinary program concerned with the impact of industrial activities on the environment and the choice of cost-effective remediation strategies. The program is designed to address critical environmental problems of basic industries, such as those involved in the extraction, conversion, and utilization of energy and mineral resources. Students acquire an appropriate blend of theory, applications, and design as well as the fundamentals necessary to maintain lifelong professional growth. Graduates are prepared to enter both the private and public sectors as environmental systems engineers or to pursue further education at the graduate level.
(College of Earth and Mineral Sciences)

* Accredited by the Applied Science Accreditation Commission of ABET, 111Market Place, Suite 1050, Baltimore, MD 21202-4012; telephone 410-347-7700; www.abet.org.

College of Earth & Mineral Sciences

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

General Engineering (Start at any Campus and Finish: Abington, Brandywine, Dubois, Hazleton)

The bachelor of science degree program in General Engineering provides students with a broad foundation in engineering and the opportunity to choose a topical engineering track of study based on their interests. In this way, the degree program presents a fundamental general engineering degree with specialization in a technically and professionally relevant topic.

From this degree program, students will acquire the ability to work as members of a team toward successful attainment of a common goal, thus preparing them to work in for-profit or nonprofit organizations, or to further their studies in graduate school. Typical employment for General Engineering graduates includes positions such as engineer, product engineer, process engineer, manufacturing engineer, development engineer, and materials engineer.

Graduates of the General Engineering program will be prepared to identify, analyze, and solve engineering technical problems; apply advanced mathematical concepts appropriately to the design and analysis of processes and systems; display effective communication skills; and demonstrate the ability to work as professionals on a team and in a project environment.

Students may choose between the Applied Materials track at Penn State Dubois,  the Alternate Energy and Power Generation track at Penn State Hazleton or the Multidisciplinary Engineering Design Option at Penn State Abington or Penn State Brandywine.
(College of Engineering)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Industrial Engineering*  (Start at any Campus and Finish: Behrend)

The undergraduate program in Industrial Engineering, being the first established in the world, has a long tradition of providing a strong, technical, hands-on education in design, control, and operation of manufacturing and service processes and systems. The curriculum provides a broad-based education in manufacturing, operations research, and ergonomics through a base of mathematics, physical and engineering sciences, and laboratory and industrial experiences. It builds a strong foundation for the development of a professionally competent and versatile industrial engineer, able to function in a traditional manufacturing environment as well as in a much broader economy, including careers in financial services, communication, information technology,transportation, health care, consulting, or academia.
(Behrend College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Industrial Engineering (Start at any campus and finish: University Park)
The undergraduate program in Industrial Engineering, being the first established in the world, has a long tradition of providing a strong, technical, hands-on education in design, control, and operation of manufacturing and service processes and systems. The curriculum provides a broad-based education in manufacturing, operations research, and ergonomics through a base of mathematics, physical and engineering sciences, and laboratory and industrial experiences. It builds a strong foundation for the development of a professionally competent and versatile industrial engineer, able to function in a traditional manufacturing environment as well as in a much broader economy, including careers in financial services, communication, information technology,transportation, health care, consulting, or academia.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Interdisciplinary Business with Engineering Studies (Start at any Campus and Finish: Behrend)

This major provides students with an interdisciplinary program containing both business and engineering course content. The major includes a set of core courses that may enable a graduate to function effectively in a technical business environment. Student can choose, from a selection of modules, a set of courses designed to enable a student to function in a specific business or technical area. The modules provide an entry-level set of skills in the areas of accounting and finance, supply chain management, quality control, technical sales, or product design and manufacture.
(The Behrend College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Materials Science and Engineering (Start at any Campus and Finish: University Park)

In addition to the traditional engineering applications of metals, ceramics, semiconductors, and polymers, new materials and composites must be developed by materials scientists to aid progress in communications, computing, electronics, biomedicine, transportation, aerospace, defense, and the production and efficient use of energy. Materials Science and Engineering provides students with a well-rounded engineering education, with specific emphasis on materials science and engineering in order to meet the needs of industry, academia, and government; conduct research at the frontiers of the field; and provide an integrating and leadership role to the broad multidisciplinary materials community.
(College of Earth and Mineral Sciences)

College of Earth & Mineral Sciences

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Mechanical Engineering (Start at any Campus and Finish: Harrisburg)

Built upon a broad foundation in physics, chemistry, and mathematics, this major has the objective of educating graduates to be problem solvers. Graduates of this program will have had opportunities to learn about applying scientific principles, engineering analysis, and engineering design to solve unstructured problems that are typical of those found in mechanical engineering. The major helps graduates prepare for a lifelong productive career, whether in professional practice, graduate school, or some other career path. Graduates will have had opportunities to learn how to work with others toward a common goal, to clearly express their ideas in written and verbal form, and to be independent and capable of adapting to the continuously changing technology of the work environment.
(Capital College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Mechanical Engineering (Start at any Campus and Finish: Behrend)

Built upon a broad foundation in physics, chemistry, and mathematics, this major has the objective of educating graduates to be problem solvers. Graduates of this program will have had opportunities to learn about applying scientific principles, engineering analysis, and engineering design to solve unstructured problems that are typical of those found in mechanical engineering. The major helps graduates prepare for a lifelong productive career, whether in professional practice, graduate school, or some other career path. Graduates will have had opportunities to learn how to work with others toward a common goal, to clearly express their ideas in written and verbal form, and to be independent and capable of adapting to the continuously changing technology of the work environment.
(The Behrend College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Mechanical Engineering (Start at any Campus and Finish: Berks)

Built upon a broad foundation in physics, chemistry, and mathematics, this major has the objective of educating graduates to be problem solvers. Graduates of this program will have had opportunities to learn about applying scientific principles, engineering analysis, and engineering design to solve unstructured problems that are typical of those found in mechanical engineering. The major helps graduates prepare for a lifelong productive career, whether in professional practice, graduate school, or some other career path. Graduates will have had opportunities to learn how to work with others toward a common goal, to clearly express their ideas in written and verbal form, and to be independent and capable of adapting to the continuously changing technology of the work environment.
(Berks College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Mechanical Engineering (Start at any Campus and Finish: University Park)

Mechanical Engineering is one of the broadest engineering disciplines and is central in many new technological developments. Mechanical engineers create things that help improve the health, happiness and safety of our everyday lives such as biomedical devices, aircraft propulsion, and ways to store renewable energies. Mechanical engineering is divided into two broad areas: mechanical systems and thermal systems. Mechanical systems include the design of mechanisms and the analysis of the strength and wear of materials. Thermal systems include methods of energy conversions, heat transfer and fluid flow.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Mining Engineering (Start at any Campus and Finish: University Park)

This major has been designed to enable students to apply the fundamentals necessary to achieve lifelong professional growth. Upon completion of the program, graduates will be able to pursue employment opportunities in both the private and public sectors as mining engineers, or will be able to pursue advanced education. Graduates of the program will be prepared to perform in the various steps of mineral extraction, including exploration, evaluation, development, recovery, and processing. The mining engineering faculty is committed to an interactive teaching and learning environment to ensure that the student plays an active role in the learning process. The General Education opportunities are sufficiently broad and diverse in nature and scope to enable the student to tailor the educational experience to particular interests, backgrounds, and expected roles in society.
(College of Earth and Mineral Sciences)

College of Earth & Mineral Sciences

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Nuclear Engineering (Start at any Campus and Finish: University Park)

The overall educational objective of the Nuclear Engineering program is to help our graduates prepare to function effectively in a wide range of career paths in nuclear engineering. The technical part of the curriculum emphasizes power engineering, which refers to complex systems used to generate electricity. Because our emphasis in power engineering is strong, and because a shortage for this expertise exists in the industry, generally the industry values our graduates highly.

We recognize that nuclear science is an important growth area. We constantly assess and review the needs of our undergraduate students and their most frequent employers and use this feedback to consider revisions to our curriculum so that it is responsive to the needs of our constituents.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Petroleum and Natural Gas Engineering (Start at any Campus and Finish: University Park)

This major has been designed to equip students with the fundamentals necessary to achieve lifelong professional growth. Graduates are prepared to enter both the private and public sectors as petroleum and natural gas engineers, or to pursue further education at the graduate level.
(College of Earth and Mineral Sciences)

College of Earth & Mineral Sciences

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Rail Transportation Engineering ( Start at any campus and Finish: Altoona)

This major provides disciplinary knowledge in engineering design and focuses on maintenance and management skills required by the rail industry. The program provides study in the major areas associated with the design, operation, and maintenance of rail systems, including the engineering of rail and track structures, basic rail operating practices and safety, wheel/track dynamics, construction and maintenance of railroad infrastructure, and basic railroad communications signals.
(Altoona College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Software Engineering (Start and Finish at Behrend; Start and Finish at World Campus)

This major provides students with a strong foundation in software engineering through combination of classroom study, software development experience, and design projects. Design, analysis, verification, and maintenance of software systems are stressed. Built upon a core of science and mathematics courses, this major has the objective of educating graduates to be problem solvers. Students acquire the ability to work as members of a team, preparing them for work in industry or further study in graduate school. In addition, written and oral communication skills are developed, culminating in a senior design project that stresses communication as well as engineering content.
(The Behrend College)

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.

Surveying Engineering (Start at any Campus and Finish: Wilkes-Barre)

The Surveying Engineering major provides a basic undergraduate education required for private and public service in the profession of surveying. Particular emphasis is placed on fundamental surveying principles. Instruction is provided in the main divisions of surveying, including land surveying, mapping, photogrammetry, data analysis and adjustment, geodesy and map projection coordinate systems, remote sensing, geographic information systems, and land development. Students study various data collection techniques using surveying tools including total stations, levels, softcopy photogrammetry, satellite imagery, and the global positioning system (GPS). They also study legal principles related to land surveying, professional ethics, applications for Geographic Information Systems (GIS) in surveying, and data management techniques. Through elective courses, students can specialize in the areas of GIS, photogrammetry, remote sensing, land surveying, and geodesy. In projects and capstone courses, students will design measurement systems, alignments, land information systems, and land development.
(College of Engineering)

College of Engineering

Please see the Basic Admissions Requirements page for more information about high school and transfer requirements.