Penryn Maths Tutors and Penryn Maths Tuition

Personal Description:
Friendly, simple person with a proven track record. Though heavily experienced in teaching, always experimenting about ways in which current students learn and hence posses a wide variety of ways to cater to different learning needs of different students.

Have helped Advanced Level students, university students, post grads etc

Teaching Experience:
More than 40 years experience as a university lecturer and tutor in UK, Singapore and Sri Lanka. Also have conducted private tuition classes (individual and group) for GCSE and A/L. Further, have worked as a researcher in International Research Institutes - all these experiences ensure you get a unique learning experience.

Tutoring Approach:
A novel approach which is student centered and outcome based. Includes many real world examples.

This new approach will ensure that learning become fun.

Subjects

Personal Description:
I am a Mathematics graduate from Cambridge University. Since 2009, I have been successfully tutoring Mathematics full-time to well over 300 pupils, with about 95% of my students achieving or surpassing their desired grades.
Before that, I worked in the IT industry, initially for a large corporation and then for an independent software house. I later formed my own company, specialising in developing applications for small- to medium-sized companies.
I study extensively to keep up to date with the latest mathematical ideas and educational trends. I ensure that I am familiar with the most recent syllabuses.
Outside work, my main interest is music, particularly singing. I belong to two choirs, one of which I am chairman.

Teaching Experience:
I teach exclusively one-to-one, as I believe that provides the best outcome for learning Mathematics. Due to the Covid-19 pandemic, I currently tutor exclusively online, using the applications Zoom for communication and bitpaper for whiteboard. I am available for home schooling: please contact me for rates.
My experience covers:
A-Level - Edexcel, AQA, OCR/OCR-MEI and Pre-U

Further Maths - Core Pure, FM1/2, FS1/2, FP1/2, D1/2

University entrance exams:

STEP
Oxford Maths Admissions Test
Advanced Extension Award

International Baccalaureate (IB) - Standard and Higher

Undergraduate topics - please inquire for details.

Tutoring Approach:
I believe in tailoring the teaching approach to each student's needs and individual learning style. For school children and university students, I discuss their aims with them - and with their parents, if required - to determine what topics need additional tuition and then to work out the appropriate programme. I advocate continuous assessment to measure the student's progress. Closer to exams, the pupils will work through focused papers. At this stage, strategic choices may be made to concentrate on the pupil's strengths.
My core teaching is for A levels. I have discovered that certain topics in the new syllabus often require extra explanation and practice. These are:
Pure: Logs, integration, and trigonometry
Statistics: Hypothesis testing
Mechanics: Forces and projectiles
For adults, I work with them to develop a personalised programme to enable them to achieve their goals. This may mean working towards a specific qualification they need.
I have great passion for and a deep knowledge of Mathematics. My aim is always to get my students to enjoy the subject. Most importantly, they are encouraged to gain confidence in their own abilities by building on what they feel comfortable with. I believe that the right teacher can undo wrong learning very quickly.
Although online currently, lessons would normally take place at the student's home, or at my home in Kingston, where I have a quiet study. Assignments and homework are an integral part of my teaching: there can be no improvement without practice.

Subjects

Personal Description:
Experienced and well qualified tutor in secondary, adult and university Maths and Physics.
With a positive attitude and engaging personality I get on well with my students.
I have also tutored students with dyslexia and autism related conditions and aware of modern educational SEN practices in this regards.

Teaching Experience:
Tutor with over 15 years adult college training and tutor experience.
Can tutor from Nationals 4/5 through to Advanced Higher, as well as GCSE/iGCSE, A-Level, IB.
Also tutor mature students and graduate level University and Colleges NC courses.
Cambridge Entrance exams STEP (paper-1 and paper-2 only).
Registered STEM Ambassador (East of Scotland).

Tutoring Approach:
I believe in putting the students interest first and ensuring that they work at
a pace with which they are comfortable.

Regular reports on progress are available to guardians.

Available daytime, evenings and weekend (presently ONLINE only)
I offer tutor online lessons via Skype/ whiteboard app- very easy at no extra cost to students.

Subjects

Personal Description:
I am passionate about education, both theory and practical implementation, I have extensive experience working with adults and children specializing in teaching English as a foreign language. I have attended numerous courses and conferences to improve and develop my skills. I enjoy languages and have travelled extensively in Europe to improve my skills.

I love teaching my native language, which is Russian.

I also worked in a British secondary school for 5 years, and then I successfully completed PGCE Maths Secondary. Now I work as a Maths teacher in a secondary school.

Teaching Experience:
- September 2020 - June 2021 - PGCE Maths Secondary
-December 12 until now Skype lessons (Russian, English as a foreign language, Maths since September 2018; all ages)
- January 20 - July 20 SKE in Maths
- July 14 - August 14 Summer Camp at Concorde International, UK (teaching English as foreign language)
-April14 - August 19 Christopher Whitehead Language College ( teaching Russian GCSE, Russian A-Level, teaching assistant in Maths, English and Science)
-July 13 - August 13 Summer Camp at Concorde International, UK (teaching English as foreign language)
-December 12 until now Skype lessons (Russian, English as a foreign language)
-October 12 - November 12 CELTA course (grade B)
-Sept 09 - Aug 12: English teacher at Moscow Secondary School - The centre of Education 'Marino' No 491'
-Oct 08 - Aug 09: A Pedagogue of additional Education at Moscow Secondary School - The centre of Education 'Marino' 491 (teaching English to children of various ages)
- July 08 - May 09: English teacher at Moscow Language School 'Franglais' (teaching adults)
- July 08: English teacher at Moscow Language School 'Big Ben' (teaching adults)
- March - May 08: English teacher at Cherepovets Language School 'Dialogue' (teaching adults)
- Jan - Jun 08: English teacher at Cherepovets Secondary School No. 21
- Sept 07 - Jan 08: English teacher & secretary at the Department of Foreign Languages at Cherepovets State University
- Sep 06 - April 07 English teacher at Cherepovets 'House of Knowledge' (teaching children aged 4 - 6)
- Jun 06 English teacher at Cherepovets Summer Camp (voluntary work)
LANGUAGES

Tutoring Approach:
I aim to provide you with a tailored programme that is best suited to your individual needs.

Subjects

Personal Description:
Post doctoral researcher at University of Sheffield, working to improve mathematical computer models which predict onset of heart disease.

I recently completed a PhD in Bioengineering at Imperial College London, carrying out mathematical research on heart disease. My first degree was in Maths at the same university, and I took a Masters in Biomedical Research in between.

I attended both a state school and a top boarding school and am comfortable to cover topics on and off the standard syllabus.

I am a very fun, friendly person with a wide range of activities and hobbies from inline skating to singing and playing the violin.

Teaching Experience:
I have tutored A-level maths privately for a few years, and also spent several weeks as a teaching assistant in a secondary school during my undergraduate degree as part of the Student Associates Scheme. Many of my contemporaries from university are science and mathematics teachers across England and overseas, and I periodically discuss teaching methods and curriculum changes with them.

During my PhD, I led undergraduate tutorials and problems classes in the Mathematics and several Engineering departments, teaching undergraduates from 1st year to 4th year. The courses include Mathematical Methods, Matlab, Fluid Mechanics, PDEs, Modelling in Biology, Heat and Mass Transfer. I also carried out 1-1 tuition for undergraduates at departmental request. I have supervised a number of undergraduate and masters research projects and summer students.

Tutoring Approach:
I am a very approachable person and I prefer interactive sessions, although I can tailor the tuition style to the individual.

A first meeting would involve an informal chat for the student and I to get more familiar with his/her needs and style of working, and everything follows from there.

Subjects

Personal Description:
I am a primary school tutor from Yorkshire and a modern foreign languages graduate from the University of Edinburgh. I have spent time teaching EFL in France and Spain and primary subjects in the UK both in schools and as a private tutor. I am now offering primary tuition services online in York during this time when parents might need to be working from home and need extra support with their child's homework.

Teaching Experience:
I taught as a private tutor in Salamanca whilst studying for my degree and for one year in Barcelona following this in a nursery, primary and secondary school. I additionally taught in two primary schools in Paris. I have worked as both a teaching assistant in the UK and as an English as a foreign language tutor in a Languages College. I have a PGCE in primary education and now teach in schools in and around York.

Tutoring Approach:
I have had experience of teaching all age groups from early primary to adults, of planning lessons and carrying out assessments. I know how to encourage all students to achieve their full potential and believe that appropriate challenge and enjoyment of learning is the key towards achieving success. I have a positive outlook and aim to develop a good rapport with all pupils and create a cooperative and calm atmosphere. It is my aim to deliver exciting and engaging lessons using familiar, real life experiences, engaging and fun games and tailored resources using a variety of teaching methods best suited to each individual child. I am patient and flexible with my time and I am willing to persevere in order to ensure that all students have fun whilst succeeding in reaching their goals.

Subjects

Personal Description:
Teaching is my passion. I have made higher salaries in other lines of work- I choose to tutor because it makes me happy! Therefore I don't just do this for the money, if a student isn't making progress then I will always tell clients exactly that. My primary aim is to help people, and if it isn't working, you'll get nothing but honesty from me!

Exam Results

I take great pride in the results of my students. Whether it be Year 6 SATS, entrance exams, GCSE Maths or many others, the greatest joy I feel is hearing good news on results day. To hear that I've managed to help someone change their life forever in a positive way is a high that I am constantly chasing.

Here are some of my student's recent achievements in major exams:

GCSE Maths

(Grade on the left is the student's grade before lesson one, grade on the right is the confirmed GCSE result)

GCSE Maths (2023)

1 student from a 4 (C) ----> 8 (A*)
1 student from a 4 (C) ----> 7 (A)
1 student from a 2 (E) ----> 5 (C+/B-)
2 students from a 3 (D) ----> 5 (C+/B-)
1 student from a 2 (E) ----> 4 (C)
1 student from a 1 (F) ----> 3 (D)
1 student from a 3 (D) ----> 4 (C)

GCSE Maths (2022)

1 student from an 8 (A*) ----> 9 (A**)
2 students from a 3 (D) ----> 5 (C+/B-)
1 student from a 1 (F) ----> 4 (C)
1 student from a 4 (C) ----> 6 (B+/A-)
1 student from a 2 (E) ----> 2(E) (started tuition just 6 weeks before exams)

GCSE Maths (2021)

1 student from a 2 (E) ----> 6 (B+/A-)
1 student from a 5 (C+/B-) ----> 6 (B+/A-)
1 student from a 3 (D) ----> 4 (C)
1 student from a 2 (E) ----> 4 (C)
1 student from a 2 (E) ----> 3 (D)

GCSE Maths (2020)
All exams were cancelled due to the pandemic

GCSE Maths (2019)

1 student from a 5 (C+/B-) ----> 6 (B+/A-)
1 student from a 2 (E) ----> 4 (C)
1 student from a 1 (F) ----> 4 (C)

GCSE Maths (2018)

1 student from a 3 (D) ----> 7 (A)
1 student from a 6 (B) ----> 7 (A)
1 student from a 2 (E) ----> 5 (C+/B-)
2 students from a 3 (D) ----> 5 (C+/B-)
1 student from a 4 (C) ----> 5 (C+/B-)
1 student from a 2 (E) ----> 3 (D)

GCSE Maths (2017)

3 students from a 5 (C+/B-) ----> 6 (B+/A-)
2 students from a 3 (D) ----> 5 (C+/B-)
1 student from a 4 (C) ----> 6 (B+/A-)

Year 6 SATS

(Grade on the left is the student's grade before lesson one, grade on the right is the confirmed SATS result)

Year 6 SATS (2019)

1 student from expected standard ----> above expectations
2 students from below expectations ----> expected standard

Year 6 SATS (2018)

1 student from expected standard ----> above expectations
3 students from below expectations ----> expected standard

Year 6 SATS (2017)

1 student from expected standard ----> above expectations
1 student from below expectations ----> expected standard

Heckmondwike Grammar Entrance Tests

3 students passed
1 student failed
75% pass rate

QTS (Qualified Teacher Status)

2 students passed on their first attempt
0 students failed
100% pass rate

Teaching Experience:
Over the last 5 years I have been teaching Maths from within my own home.

Tutoring Approach:
The goal of each and every lesson is to make the sessions as interactive as possible. By engaging pupils at every opportunity, the lessons become really enjoyable with the students learning an awful lot more than if they were simply to be handed workbooks. There are many tutors that will take this approach and just watch a student go at it, I prefer to be much more involved! I also make new learning games everyday and this is a big reason why my students have been so successful at all ages.

Subjects

Personal Description:
I am a dedicated teacher and tutor who is passionate about education and the progression of students to achieve their maximum potential. Currently Head of Economics, with 10 years experience in the classroom teaching A-Level and GCSE Business, Economics and Financial Education.

Teaching Experience:
I am currently Head of Economics in a highly successful inner London secondary school. I have taught for 10 years across various exam boards and also have experience as an A-Level examiner for AQA. I am a co-author for the most recent GCSE Economics workbook by published by Hodder Education.

My previous experience includes working as an Academic Mentor for Economics and Business Studies in a Sixth Form College. My undergraduate degree was in BSc Economics from City University London. I also completed my PGCE in Business and Economics Education at the Institute of Education, UCL.

I have worked with many A-Level and GCSE students across London to achieve different objectives, ranging from understanding key diagrams to mastering exam technique!

I have been able to witness first-hand the positive impact of tuition and love the opportunity to expand the knowledge and experiences of the students that I meet.

Tutoring Approach:
I believe in a student - centred approach, focusing on building confidence and equipping students to be independent learners. I use current Business and Economics news in sessions, to help students understand different theories and concepts. I use past papers and practice questions to help students develop their exam technique and exam assessment objectives.

I have had experience tutoring online using platforms such as Zoom, Microsoft Teams and Google Meets. I ensure that lessons are engaging use different methods to ensure students are still building their knowledge and understanding of the topic.

Subjects

Personal Description:
I welcome children into a positive, stimulating environment, where each child is valued and can learn effectively. I am proactive, ambitious, have a sense of humour, honest, enthusiastic and conscientious of others as well as a valued team member. I believe that effective learning happens when children are inspired, motivated and challenged in a positive environment where they feel happy and praised. I have a desire to promote reading for pleasure and I love to tell stories and listen to children read. I also enjoy teaching mathematics, problem solving and making learning fun. In my spare time, I enjoy pilates as well as going for walks and socialising with friends and family.

Teaching Experience:
I have 8 years of qualified teaching experience with whole classes and 1:1. I have experience in both England and wales so have a strong m knowledge of both national curriculums. I have lots of experience working ALN children and differentiate lessons to meet every child's needs!

Tutoring Approach:
I like to develop positive relationships with children I teach and therefore I enjoy engaging with children through their personal interests and humour. I find out which areas each child requires improvement before setting a range of activities to develop their learning. I address the VAK (Visual, Auditory and Kinaesthetic) learning styles of children that I teach and use a creative approach to teaching. I like to assess individuals through games to increase engagement and encourage independent learners, aiming to increase self esteem and confidence.

Subjects

Personal Description:
My previous students have described me as relatable, friendly, and passionate about unleashing their potential, and I am determined to meet the same description by individuals I teach here. Having moved to Sheffield very recently from Manchester, I am committed to replicating positive opinions and success in any new tutees who give me the opportunity to teach them. My students are always grateful for my help, especially my son who achieved an A* in his mathematics A level last year (as well as at GCSE), despite stating he felt little interest in the subject.

As a tutor, few things are as emotionally rewarding to me as results day, and I am fervent about ensuring my new students feel the same way if given the chance.

Teaching Experience:
Throughout my academic and professional life, I have tutored individuals requiring improved understanding and practice in mathematics. Based on my observations and the fact that tutoring took up a significant amount of my time after I completed my PhD in Physics from the University of Manchester, I have accumulated a wealth of experience on how to teach a wide range of students based on their mindset, targets, and preferred methods of learning.

Tutoring Approach:
I am proud to say that my determination and techniques of making learning and revision enjoyable have allowed me to always perform as one of the best in every institution I have studied at, which is something I have noticed in many of my tutees. Since I have attended both below-average, and far above-average institutes, I am experienced in how to encourage people of various 'school-cultures' to find the drive to study and succeed.

Subjects

Personal Description:
** Available after 5pm on weekdays**
I`ve completed a PhD in Mathematics at the University of York, UK, and I'm a native Italian speaker with a strong passion for teaching.
I have 15 years of experience with one-to-one Maths tutoring to students from any level of education, and I worked for 4 years as a seminar leader in modules taught in my university department.

Teaching Experience:
I specialise in Mathematics, and I teach GCSE, A-levels, IB, and university students; I have experience with Edexcel and AQA exam boards.
As to university teaching, I specialise in probability, calculus, and mathematical analysis.
I also have experience with teaching Physics to GCSE and A-level students and Italian to adult learners.

I started teaching in 2009 as a Maths a Physics tutor for secondary school students in Italy. I started tutoring in the UK in 2017, both online and in-person, and in 2018 and 2019, I also volunteered at the City of York council as a maths teaching assistant. I've been teaching secondary school and university students for 15 years now.
Between 2017 and 2021, I worked as a seminar leader in the Maths department of the University of York for probability, calculus, and mathematical analysis modules.
In 2019, I started teaching Italian to adult learners who need support with conversation skills and grammar.

Tutoring Approach:
My aim is to make my students confident and independent in their studies.

During the introduction, I meet the student and their guardian so that we can get to know each other. I learn about their needs and aims, and we start planning the lessons.

The plan typically consists of weekly or fortnightly lessons depending on the content the student needs to cover; some students need to focus only on specific topics, while others need support throughout the year.

During the lessons, I focus both on supporting the students with the new material they have to learn and on filling the gaps they might have in order to build a solid foundation. To do that, I use worksheets that are focused on a specific topic and past exam papers that can help students prepare for tests and exams.

I organise my lessons so that the students can think of how to solve exercises while I guide them to the solution, rather than tell them what to do step by step. That way, they develop their own method to understand and study Maths and boost their confidence.

As to my Italian lessons, I base them on practice so that the students can gain more confidence, especially with listening and speaking, while strengthening their basic grammar knowledge. During the lesson, I like to create conversations aimed at practising oral comprehension and production.

Subjects

Personal Description:
I am a reliable, hardworking young man who is passionate about education. I am very relevant to the upcoming generation in terms of my ways to deliver information which are very exciting and interesting.

Teaching Experience:
I have vast experience in tutoring a variety of University and High School students mainly focusing on Economics, Accounting, Mathematics and statistics for 4 years.

Tutoring Approach:
My approach is to deeply explain the subject in question and give a technical way to answer a variety questions

Subjects

Personal Description:
I have always been incredibly passionate about learning as much as possible and I want to instil this in others.
I have high scores on my GCSEs and AS Mathematics and I am currently studying Mathematics at University.
I am a very friendly, outgoing person who enjoys teaching thoroughly.

I genuinely love what I do.

Teaching Experience:
I have been teaching since my sister was learning to talk but I first started as a private tutor at age 14. I was lucky enough to teach a class of 30 girls just after I did my GCSEs at age 17, and from there I went on to start my own business.

I worked for myself as a private maths tutor for 3 years before working at London School or Science and Technology and I am now back to private tutoring.

Tutoring Approach:
My teaching style changes depending on every student I face. I would identify as having the facilitator style which is someone who encourages self-learning by asking the student questions rather than telling them the answer.

I also specialise in last minute GCSE revision where I am able to make the subject matter seem much simpler than how it is explained in many schools.

I have done a huge amount of work with ADHD and dyslexic students so I have had to deal with about every behavioural issue there is with the utmost patience and I experience a lot of joy in learning how the students get to the answer.

I have created many lesson plans myself for ages 4-16, which include animated PowerPoints, mainly in maths but I am happy to create them for any subject.

I always begin with a game or a riddle just to get thinking cap on and then we will tackle a subject with an explanation and worked examples.

Subjects

Personal Description:
I am Sraddha an experienced Maths tutor taking sessions online and offline.

Teaching Experience:
As a math online tutor with over 3 years of experience, I specialize in guiding K-12 students from the US and UK towards academic excellence. My expertise spans various math disciplines, including algebra, geometry, calculus, statistics, and probability. I prepare students for challenging tests such as AP exams, GCSE, and A-level tests. . Utilizing online platforms like Zoom, Skype, and Google Meet, I make learning convenient and accessible.

Tutoring Approach:
Through personalized lessons and flexible scheduling, I foster a supportive environment that boosts confidence, improves problem-solving skills, and yields better grades.. With a proven track record of student success and a Master's degree in Mathematics, I'm dedicated to helping you unlock your full potential.

Subjects

Personal Description:
A second year medic at the University of Edinburgh. I graduated with 44/45 in the IB.

I did not get where I am today by myself. I had help - friends, family, and teachers. I know how much impact a teacher can have, and I just want to help where I can.

Prior to Uni, I spent 2 years in the Army developing ,training and leading frontline soldiers. I have seen people from all walks of life and am committed to developing and teaching my students as well.

Teaching Experience:
Prior to Uni, I tutored final year IB students for a year. Prior to that, I did not have any formal teaching assignments, only teaching friends or some of my soldiers when I was serving. Despite that, I have been coaching for most of my life. Since I was 15 I have been mentoring my juniors in my extra curriculars at school, so I am well versed when it comes to different methods of mentoring.

Tutoring Approach:
I enjoy getting to know my students beyond their academic needs; building a connection and seeing that they are supported in any way that I can.

I also believe in understanding rather than memorizing, so I teach my students skills that will help them approach problems logically instead of just memorizing the textbook.

I am flexible and can tailor lesson times specific to the student.

Subjects

Personal Description:
Hi! I'm Dudo-a cheerful and passionate medical student who's excited to help you succeed. I'm trilingual, fluent in English, Cantonese, and Mandarin. Having earned straight Grade 9s and 8s in my GCSEs and completed A-levels in the UK, I know what it takes to excel academically. I'm here to share the tips, strategies, and support that helped me thrive. I can't wait to meet you and support your learning journey!

Teaching Experience:
While I may not have extensive formal teaching experience, I bring a wealth of practical knowledge and proven strategies for tackling exams and tests-gained through my own academic journey. I've also spent a few months tutoring Year 7 students in mathematics, which gave me valuable insight into how to support learners effectively.

Tutoring Approach:
Want to achieve Grade 9? Consistent practice with past papers-it's that simple. Having earned straight 9s and 8s in my GCSE subjects, I understand how crucial it is to master not just the content, but the exam technique and strategy that help you "play the game" effectively.

My lesson style includes:
1. Initial group chat with students and parents: understand goals, expectations, and identify strengths and areas for improvement.
2. Pre-lesson preparation: I ask students to send me their school materials a week in advance so I can tailor the session to match their curriculum-ensuring lessons feel smooth and never overwhelming.
3. Lesson time!
4. Homework assignments: reinforce what we've covered.
5. Progress updates: I regularly share a summary of what we've covered in the group chat to keep everyone informed.

Subjects

Personal Description:
Are you ready to discover the beauty and elegance of mathematics? Whether you're struggling with algebra, puzzled by geometry, or curious about calculus, you've come to the right place! As a passionate math tutor, I'm here to make the seemingly complex concepts not only understandable but also enjoyable. With 7 years of experience as a math tutor, I've helped countless students of all levels, from primary school to university, excel in their math journey.

Teaching Experience:
With 7 years of experience as a math tutor, I've helped countless students of all levels, from primary school to university, excel in their math journey. I'm currently working in a College having GCSE classes .

Tutoring Approach:
I always try to find the best way possible to explain topics based on the learners needs .

Subjects

Personal Description:
I hold a PhD in Chemistry and am a published scientific author. I offer concierge-level tutoring for students who demand the very best results.

I have extensive experience across all major UK and international qualifications:

* IB Diploma
* AQA
* Edexcel
* OCR A
* SQA National 5
* SQA Higher
* SQA Advanced Higher

Teaching Experience:
Over fifteen years, I have guided students across KS3, KS4, GCSE, A-level and Further A-level and IB Diploma - many of whom have gone on to read Medicine, Veterinary Science, Engineering and other highly competitive degrees at leading universities, including Oxford and Cambridge.

Tutoring Approach:
I work exclusively online via Zoom, with a shared interactive whiteboard, structured homework, and direct email communication between sessions.

Each engagement begins with a diagnostic session. I assess the student's current level, identify the specific gaps in their understanding, and build a tailored programme from there. Every student receives a strategy designed around their syllabus and their individual goals.

Typical sessions combine targeted concept work and past-paper practice. Between lessons, homework is prepared and shared on the whiteboard; I follow up by email once it is ready. Progress is reviewed continuously, and the plan is adjusted accordingly.

My students are expected to invest effort between sessions and complete their homework. I work with a small, carefully selected cohort of students each term. Places are limited and not all enquiries are accepted. I hold a current PVG Scheme certificate and am fully vetted. For families who require it, I am happy to sign a non-disclosure agreement prior to any engagement. Enquiries are handled with complete confidentiality.

Subjects