BSc (Hons) Mathematics with Foundation Year

Program Overview

---

Mathematics with Foundation Year

Overview

The Mathematics with Foundation Year program is designed to help students build a strong foundation in mathematical principles, preparing them for the BSc (Hons) Mathematics Degree. This pathway is recommended for students who don't meet the prerequisites for the full honors degree.

Attendance

• Full-time
• With placement
• Four-year or five-year course

Next Enrolment

• September 2025

Introduction

The Mathematics with Foundation Year program is designed to take students to an advanced level, blending applied methods with cutting-edge themes. Students will learn to make an important contribution to the world around them, be it in science, technology, or engineering.

Course Details

Foundation Year

• Foundation Mathematics A and B: Development of mathematical and modeling skills, including algebra, transposition of formulae, coordinate systems, logarithms, introduction to calculus, problem-solving in velocity and acceleration, differentiation, integration, and matrices.
• Foundation Physics A and B: Grounding in basic physics and development of numerical problem-solving skills, including mechanics, properties of matter, wave propagation, electronics, electricity, fields, and atomic and nuclear physics.
• Introduction to Probability and Statistics: Introduction to core mathematics equivalent to A-level, including basic probability and statistics.
• Foundation IT and Study Skills: Development of IT, research, team working, presentation, and scientific reporting skills.

BSc Degree

• Course delivery: Delivered over three years or four with a placement year, exploring the core fundamentals of mathematics and consolidating A-Level knowledge before advancing skills across applied mathematics areas.
• Learning experience: Small group teaching, guided and focused help from lecturers, and applied approach to mathematics.
• Industry placement: Option to take an industry placement between years two and three, with support from tutors and assessment of final placement report.

Modules

Year One

• Probability: Building upon and extending A-Level mathematical probability knowledge and developing the subject of probability with applications.
• Analysis: Introduction to the concept of proofs and constructing simple proofs, understanding fundamental concepts of limit, continuity, differentiability, integration, and function in mathematical analysis.
• Linear Algebra: Methods and theory behind the solution of simultaneous equations, developing skills in solving linear problems using matrix methods and the concept of abstract vectors.
• Mathematical Methods 1: Building on A-Level mathematical techniques and knowledge in preparation for subsequent mathematics modules.
• Mathematical Modelling: Building upon and extending A-Level mathematical techniques, providing a mathematical foundation in support of subsequent mathematics modules.
• Mechanics and Vector Calculus: Introduction to the principles of classical mechanics and vector calculus, developing skills in solving numerical problems in mechanics and vector calculus.

Year Two

• Business and Industrial Mathematics: Experience in business and industrial working practices, solving practical mathematical problems, and working in groups to solve real-life problems.
• Mathematics Methods 2: Extending methods in differential and integral calculus, first and second-order partial differential equations, and methods in differential and integral calculus for the complex variable.
• Numerical Analysis: Presenting key solutions in optimization of numerical algorithms using the computer, including root finding, interpolation techniques, numerical calculus, and linear algebra.
• Statistics: Developing a sound knowledge in probability models and distribution theory, skills in statistics and data analysis, and awareness of the principles and scope of data analysis models.
• Dynamical Systems: Understanding nonlinear dynamics, merging mathematical analysis and numerical computation.
• Applied Mathematics 1: Introduction to tensors and tensor algebra, applying these tools to problems in fluid and structural dynamics.

Year Three

• Mathematical Methods 3: Investigating more advanced techniques of solving differential equations using methods such as Fourier and Laplace transforms, series methods, and more.
• Project: Developing a mathematical model within a challenging research theme, demonstrating understanding of the application of mathematics to one of these areas.
• Mathematical Statistics: Revisiting the foundations of statistics from a more mathematical standpoint, gaining theoretical and practical skills in mathematical statistics.
• Programming and Optimisation: Applying mathematics to a variety of problems in physics, economics, and life sciences.
• Optional Module: Operational Research or Applied Mathematics 2.

Assessment

• Coursework: 30%
• Exams: 70%
• Presentations: individual or group presentations of the final outcome to a particular assignment or brief
• Examinations: usually two hours in duration, testing material presented in lectures, workshops, and seminars
• Written assessments: class tests, reports, and evaluations
• Research project presentation: individual or group presentation of the final outcome to a particular assignment or brief
• Coursework and continuous assessment: class tests, reports, and evaluations

Requirements

• GCSE: English language and Mathematics at grade C/level 4 or above
• UCAS tariff points: 64 points where qualifications include both Mathematics and Physics to A-Level or equivalent standard, or 72 points from any subject combination without Mathematics and Physics
• A Level: 64 points where qualifications include both mathematics and physics, or 72 points from any subject combination without mathematics and physics
• BTEC Higher National Diploma: MPP for Engineering or science subjects, or MMP for subjects without mathematics and physics modules
• T level: This programme accepts the following T levels: Design and Development for Engineering and Manufacturing Maintenance, Installation and Repair for Engineering and Manufacturing Engineering, Manufacturing, Processing and Control
• Access to HE: 64 UCAS points from QAA-approved science or engineering courses
• Scottish Highers: 64 UCAS points where qualifications include both Advanced Higher level mathematics and physics, or 72 UCAS points from any subject combination without Advanced Higher level mathematics and physics
• Irish Leaving Certificate: 64 UCAS points where qualifications include both Higher Level mathematics and physics, or 72 UCAS points from any subject combination without Higher Level mathematics and physics
• European Bacclaureate: Pass in Diploma of at least 60%, to include Science, Engineering or Technology
• International Baccalaureate: 26 points including Higher Level mathematics or physics at grade 4

Tuition Fees

• Full-time home: £8,505 for Foundation Year and £9,535 for subsequent years

Additional Costs

• Books, stationery, printing, binding, and general subsistence on trips and visits

Accreditation

• This course will meet the educational requirements of the Chartered Mathematician designation, awarded by the Institute of Mathematics and its Applications, when it is followed by subsequent training and experience in employment to obtain equivalent competences to those specified by the Quality Assurance Agency (QAA) for taught masters degrees.

Program Outline

---

Degree Overview:

---

Overview:

The BSc (Hons) Mathematics with Foundation Year at the University of Salford is a four-year program (or five years with a placement year) designed to equip students with advanced mathematical skills and knowledge applicable to various fields, including science, technology, and engineering. The foundation year pathway prepares students lacking the direct entry qualifications, allowing them to build a strong foundation before progressing to the full honors degree.

---

Objectives:

• Equip students with a strong foundation in mathematics.
• Develop advanced mathematical skills and knowledge.
• Apply mathematical principles to real-world problems.
• Prepare students for careers in various fields requiring advanced mathematical skills.

---

Program Description:

The program blends theoretical, collaborative, and practical teaching methods, including:

• Tutorials and seminars on specific topics.
• Talks and lectures by academics and industry guest lecturers.
• Practical workshops for computer-based problem-based learning exercises.
• Case studies and project work.
• Group assignments.
• Online learning using Blackboard.
The program features a strong emphasis on applications of mathematics in the real world, providing students with valuable skills for solving complex problems across various industries.

---

Outline:

---

Year 1 (BSc Mathematics) - Foundation for Mathematical Knowledge:

• Probability: builds upon A-Level knowledge and develops its applications.
• Analysis: introduces proofs and fundamental concepts of mathematical analysis.
• Linear Algebra: delves into methods and theories for solving simultaneous equations.
• Mathematical Methods 1: builds upon A-Level techniques and covers differential equations with applications.
• Mathematical Modelling: provides a mathematical foundation for subsequent modules and introduces problem-solving using a symbolic computing environment.
• Mechanics and Vector Calculus: introduces principles of classical mechanics and vector calculus with problem-solving skills development.

---

Year 2 (BSc Mathematics) - Building Advanced Mathematical Skills:

• Business and Industrial Mathematics: provides experience in business and industrial working practices and solving practical mathematical problems.
• Mathematics Methods 2: expands methods in differential and integral calculus, partial differential equations, and complex variables.
• Statistics: develops knowledge in probability models and distribution theory, along with data analysis skills.
• Dynamical Systems: introduces concepts and phenomena of dynamical systems and merges mathematical analysis with numerical computation.
• Applied Mathematics 1: introduces tensors and tensor algebra and their applications in fluid and structural dynamics.

---

Year 3 (BSc Mathematics) - Applying Mathematical Knowledge:

• Mathematical Methods 3: explores complex techniques for solving differential equations using advanced methods like Fourier and Laplace transforms, as well as series methods.
• Project: allows students to develop mathematical models within challenging research themes relevant to society, like climate, nanotechnology, renewable energy, and sustainable economics.
• Mathematical Statistics: revisits the foundations of statistics with a more mathematical focus, providing skills in theoretical and practical statistics.
• Programming and Optimisation: applies mathematics to problems in various fields like physics, economics, and life sciences.
• Optional Module: students choose one from Operational Research or Applied Mathematics 2.
• Operational Research: develops skills to construct models for finding solutions to complex decision-making problems.
• Applied Mathematics 2: focuses on applying mathematics to problems in fluid and structural dynamics.

---

Assessment:

• 30% coursework and 70% exams in most modules.
• Some modules use 50% coursework/50% exam weighting.
• Assessments include presentations, written assessments, research project presentations, and examinations.

---

Teaching:

• Tutorials and seminars on specific topics.
• Talks and lectures by academics and industry guest lecturers.
• Practical workshops for computer-based problem-based learning exercises.
• Case studies and project work.
• Group assignments.
• Online learning using Blackboard.

---

Careers:

• Finance and investments
• Market research
• Meteorology
• Engineering
• Data analytics
• Business operations
• Graduates receive a significant discount on postgraduate studies at Salford.
• The program focuses on various applications of mathematics, making it relevant to today's society.