Page 66 - Best Doctoral Certificate Courses - Eligibility, Fees, Duration, Career Options

Offered by

The Hong Kong Polytechnic University, Hong Kong via Edx

Certificate

Knowledge Management and Big Data in Business

The Knowledge Management and Big Data in Business program presented by the platform of Edx provides learning freedom to all candidates interested in business and management. The course is an 8-week learning program. Students should invest 6-8 hours weekly to complete this management and big data business certificate programme. The Hong Kong Polytechnic University has designed the Knowledge Management and Big Data in Business training in collaboration with Edx. Interested candidates willing to study in this management training program will learn about subjects such as management and business.

The online course on big data in business and knowledge about management provides introductory-level knowledge about the concepts related to the field. There are two options to pursue the Verified Knowledge Management and Big Data in Business certification, namely, verified and audit. In the verified mode, the learners can get this certification program after paying the required fee. Aspirants can avail themselves of this program free of cost in the free audit mode.

8 Weeks

Beginner

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Skills Covered:

Knowledge of Big Data

Offered by

Penn via Edx

Certificate

Big Data and Education

There has been a surge in the use of online and software-based learning tools and their applications in the education sector in recent times. This has resulted in an increase in data generated that can be used for improving educational effectiveness. This can also help in supporting research for learning. The Big Data and Education by edX is one such initiative to make candidates learn about the methods and key analytics techniques for data mining and its uses in education. This Big Data and Education certification will teach candidates about the various techniques and methods being used by researchers and developers in the data mining of the education domain.

The various methods covered in the Big Data and Education certification syllabus are using and applying Python and other tools such as RapidMiner etc. The practical aspects of this like determining the trustworthiness and other application shortcomings will also be covered. The learners have two modes to join the programme; free and verified. In the verified mode, the learners need to pay the fee and will get the certificate whereas in the audit mode, the candidates can join the course free of cost and get a limited duration.

8 Weeks

Expert

Compare

Skills Covered:

Knowledge of Big Data

Offered by

The University of Texas Medical Branch, Galveston via Edx

Certificate

Biostatistics for Big Data Applications

The Biostatistics for Big Data Applications training starts with statistical concepts and terminology, and a brief introduction to the R statistical software package, creating a foundation for learners to build on. Later on, the fundamental components of the bio statistical methodologies used in both omics and population health research are discussed.

Examples will be discussed after each topic in the Biostatistics for Big Data Applications certification syllabus. There will also be self-assessment opportunities for learners to gauge their understanding. Moreover, to improve their R programming skills, participants can undertake practice exercises and use real datasets that will be provided to them.

The Biostatistics for Big Data Applications programme is developed by the University of Texas Medical Branch (UTMB). The video lectures are delivered in English, and their transcripts are also available only in English. To complete the programme comfortably within eight weeks, learners should spend around 2-3 every week, studying.

8 Weeks

Beginner

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Skills Covered:

Statistical skills R Programming

Offered by

Upskillist

Certificate

Data Analytics Certification Course

Data Analytics Certification Course is a highly relevant training program that explores a wide range of topics under the broad spectrum of data analytics. The course has been designed for the online platform, and you can avail free trial. Every week you will be presented with modules with a higher level of difficulty that will train you with practical and theoretical knowledge.

One of the essential aspects of the Data Analytics Certification program is that it is a globally accredited certification and live educator support to all students. The course curriculum has been carefully curated to bring international focus and a high level of understanding. You will also get the benefit of regular evaluation and assessments through exams and tests.

The Data Analytics Certification Course is offered by Upskillist to help you gain a solid understanding of the field and build a foundation in statistics. It offers flexibility by allowing you to choose your class schedule and pause your course at any given time.

8 Weeks

₹ 299

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Skills Covered:

Statistical skills R Programming Knowledge of Excel Tableau knowledge

Offered by

NITTTR Chandigarh via Swayam

Certificate

Big Data Analytics For Smart Grid

The Big Data Analytics For Smart Grid certification course is an 8-week course that uses the concepts of Python programming language is an open-source software to demonstrate the use of Big Data Analytics in smart grid systems. The data in today’s world is influenced by the fast developments taking place in cloud computing and digital technology involving human activity, communications, sensors and digital equipment.

The Big Data Analytics For Smart Grid training will involve case studies and begins with the introduction and importance of such analysis with data collection through intelligent devices, machine learning, deep learning, and its associated algorithms.

The coursework is intended for both academic based attendees such as students, faculty and industry professionals. This course is supported and framed in collaboration with industries such as IBM and Opal-RT. This Big Data Analytics For Smart Grid programme aims to explore the issues arising in the processing and analysis of large volumes of data which is challenging to be done in a structured way.

8 Weeks

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Skills Covered:

Machine learning Knowledge of Big Data Knowledge of cloud computing Data science knowledge

Offered by

361 DM via TCS iON

Certificate

Certificate Program in Big Data Technologies

Data analysis is important for research and making further policies for the development of the organization. Extracting, analyzing, and processing data from complex data set can become an easy task through Big data technologies. The challenging task of analyzing structured, semi-structured, and unstructured data can become manageable through the course by TCS iON. The certificate program in Big Data Technologies is a self-paced course available for IT professionals or data analysts on the TCS iON portal. This is the online course of two months jointly organized by TCS iON and 361° minds.

Certificate Program in Big Data Technologies training shall guide the learners for working and analyzing the complex data using the software. The course needs the commitment of 8-9 hours per week in the duration of 8 weeks to complete the course on time. The certification course is designed in a way that it shall provide the knowledge from basic to advanced level to the learners about analyzing complex data sets. The Certificate Program in Big Data Technologies certification syllabus consists of modules and assessments preparing learners for the TCS iON Procert assessment. The assessment shall open the gates for multiple opportunities as a data analyst. After the completion of the course, the learner shall receive Certificate Program in Big Data Technologies certification by TCS and 361° minds.

8 Weeks

₹ 18,000

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Skills Covered:

Data science knowledge

Offered by

MSLS Manipal

Certificate

Certificate Course in Bioinformatics

Bioinformatics is widely used in biomedical development and research work. The Certificate Course in Bioinformatics aims to teach the concepts of this discipline which applies computational techniques and theoretical procedures to analyze biomedical or biological data. The program will enable learners to utilize advanced technology to leverage the growing store of biological information.

Computers are used to work on genetic information that can help answer questions related to human health. The Bioinformatics certification course by MSLS will train the students to become competent in using information technology to extract, analyze, utilize, store, organize and interpret biological data. Learners will understand bioinformatics concepts like integrating molecular biology, computer science, and mathematics.

The Certificate Course in Bioinformatics by MSLS is designed to provide theoretical training along with hands-on sessions, assignments, and projects to make industry-ready bioinformatics professionals. Candidates will understand the application of bioinformatics in all domains of biological sciences.

8 Weeks

₹ 11,000

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Skills Covered:

Knowledge of bioinformatics

Offered by

MIT Cambridge via Edx

Certificate

Molecular Biology – Part 3: RNA Processing and Translation

The Molecular Biology - Part 3: RNA Processing and Translation course by edX is the third and final part of their Molecular Biology programme. In this programme, you will learn about the mRNA translation to protein, a crucial portion of Biology’s central dogma. You will also see how RNA splicing or RNA turnover affects the outcome of this translation.

RNA processing mechanisms also influence gene expression. You will learn about these mechanisms in extensive detail with the Molecular Biology - Part 3: RNA Processing and Translation training course. It is an eight-week, advanced-level, self-paced learning programme that will help you master design skills in biological experimenting, and enhance your scientific thinking. You need to study only four to eight hours every week.

The faculty includes professors from the Department of Biology, Massachusetts Institute of Technology (MIT). Each instructor for the Molecular Biology - Part 3: RNA Processing and Translation programme is an expert in his/her respective domain. They will deliver video lectures in English. Video transcripts are also available in two languages: English and Chinese. The programme can be taken by the candidates in two modes, namely, free and paid modes. In the free mode, the learners will be provided with limited access to the programme.

8 Weeks

Expert

₹ Free

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Skills Covered:

Knowledge of Biology

Offered by

Swiss Federal Institute of Technology Lausanne via Edx

Certificate

Cellular Mechanisms Of Brain Function

The Cellular Mechanisms of Brain Function programme by edX provides intelligence to the learners in the concepts of brain functions which include membrane potential, cable properties, ion channels, action potential, whole-cell recordings, voltage-gaining kinetics, synaptic transmission, neurotransmitter release, electron microscopy, presynaptic dynamics, glutamate receptors, synaptic plasticity, benzodiazepines, and dendritic spines.

This programme helps the candidate to understand the fundamental concepts of neuroscience which are related to the functions of the mammalian brain. Cellular Mechanisms of Brain Function course also provides an outline of the biophysical mechanisms of signalling in the neurons. The candidate will also learn about various receptors in the brain. The brain functions are studied through various biophysical mechanisms using mice. Various modern methods are also discussed in this programme to study the workings of the mammalian brain.

The verified and shareable certificate is provided to all the candidates on completion of this programme. The certificate can be easily shared to a resume or CV. It can also be shared with the LinkedIn profile of the learner. There are two varied options for candidates to enrol in the programme; free or by paying the prescribed fee. When enrolling for free, the learners will get access only for a limited period.

8 Weeks

Intermediate

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Skills Covered:

Knowledge of Biology

Offered by

Doane University, Crete via Edx

Certificate

Medical Cannabis

Offered by Doane University, Medical Cannabis is an 8-week self-paced online certification course. The course is delivered via edX and available for free to enrol in. The Medical Cannabis certification course focuses on medical and scientific topics related to therapeutic uses, the bio-availability of medical cannabis, and its delivery methods. It also emphasise how major and minor cannabinoids link with the endocannabinoid system. By pursuing the Medical Cannabis certification by Doane University via edX, learners will have a solid understanding of the compounds in cannabis.

Students will explore various crucial topics and methods related to medical cannabis in the Medical Cannabis certification syllabus. They will also gain an understanding of the entourage effect, drug tolerance, side effects, dose-response relationships, and dependence. The Medical Cannabis training programme is an introductory course delivered through videos and graded assignments. Individuals looking to master the key concepts of medical cannabis and related medical and scientific topics can opt for the Medical Cannabis online course. Candidates may enrol in the free audit track with limited access or they may upgrade to the paid verified track.

8 Weeks

Beginner

₹ Free

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Skills Covered:

Knowledge of healthcare sciences

Offered by

IMD

Certificate

Business Analytics for Leaders Online

There is almost nothing in a company today that is not affected by data analytics, regardless of industry. The 8 weeks Business Analytics for Leaders online course provided by IMD offers candidates with a strategic, high-level grasp of digital analytics and big data analytics. Candidates will also receive a quick introduction to the use of Machine Learning and Artificial Intelligence in business, which may be applied to their situation.

Business Analytics for Leaders course provides a high-level grasp of how to apply business analytics strategically. The course offers a uniquely practical approach, with tips, tools, and inputs that can be applied right away in the day-to-day job. IMD offers a high-quality learning environment.

The Business Analytics for Leaders online syllabus helps to understand how to apply business analytics to gain a competitive advantage. Candidates will be able to identify the various degrees of analytics development and know where their business sits in a competitive and dynamic market. By the end of the course, candidates will be awarded a Business Analytics for Leaders online training certificate from IMD.

8 Weeks

05 October 2025 - 29 November 2025

2,950

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Skills Covered:

Business analytics knowledge Knowledge of Artificial Intelligence

Offered by

UCT Cape Town via GetSmarter

Certificate

Business Analytics

Companies are attempting to harness innovative technologies in order to maximize productivity, grow into new marketplaces, and compete for a worldwide digitally informed customer base as the Fourth Industrial Revolution proceeds. Organizations are trying to use the flood of data statistics for better decision-making due to the inevitable need to be at the forefront of technology and competition. The Business Analytics online course is a University of Cape Town offering eight weeks program.

There is a growing demand for people who can comprehend and use data analytics since there is a scarcity of experienced people to clean, integrate, and extract useful information from big data. The Business Analytics Training enhances business intelligence skills by using statistical approaches to data sets in order to extract valuable insights and exercise informed decision-making.

The Business Analytics Syllabus explores storytelling, data visualisation and teaches about Structured Query Language(SQL). The course introduces various market-leading analytics and business intelligence software and teaches how to use them for making informed business decisions.

8 Weeks

₹ 76,299

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Skills Covered:

Business analytics knowledge

Offered by

Cooper Union via Edx

Certificate

Preparing for CLEP Chemistry: Part 2

From periodic tables to matter malleability, the Preparing for CLEP Chemistry: Part 2 certification course helps its learners learn and revise concepts usually questioned in the CLEP exam. Rather than forcing students to learn, this course allows the ward to pick up ideas at their own pace with pre-recorded videos. Fundamental know-how of high-school level Chemistry and Mathematics is necessary to pursue the training.

Concepts included in the Preparing for CLEP Chemistry: Part 2 Certification Syllabus are atomic theories, bonding, electrochemistry, equilibrium, and stoichiometry. Students will understand the structural influences on particle arrangement within solid, liquid, or gaseous substances. Through discussion forums, students can interact with peers and create study groups.

The Preparing for CLEP Chemistry: Part 2 program is taught by Ms. Allison Tau, Mr. Lori Zaikowski, and Mr. Ruben Savisky. Developed by the Cooper Union, the assignments and quizzes allotted by the course are auto-graded for students to gauge their progress. Additionally, a verified certificate is available to students by paying a nominal fee.

8 Weeks

Beginner

Compare

Skills Covered:

Knowledge of Chemistry

Offered by

Duke University, Durham via Coursera

Certificate

Introduction to Chemistry: Structures and Solutions

Introduction to Chemistry: Structures and Solutions certification is a beginner-level programme requiring only 16 hours that is conducted over 8 weeks. The course content has been built by Duke University whereas the completion certificate is the department of the online provider Coursera.

Introduction to Chemistry: Structures and Solutions training is an introductory level course that can even be suitable to candidates who have zero or limited knowledge of chemistry. This certification course belongs to the course category of physical science and engineering on Coursera. The introductory concepts will be available to the candidates in the form of short reading, or videos, or even practice exercises. Both the course, and its mentors are wonderful, and thus the participants will learn the concepts with ease throughout this online course.

8 Weeks

Beginner

₹ Free

Compare

Skills Covered:

Knowledge of Chemistry

Offered by

Skill Lync

Certificate

Advanced Structural Analysis using ANSYS Workbench

The Advanced Structural Analysis using ANSYS Workbench course covers all the essential lessons and skills of the ANSYS Workbench software. You will become fluent in using it for Finite Element Analysis (FEA), performing thermal, structural, and vibrational analysis, simulations, and analysing the results. The Advanced Structural Analysis using ANSYS Workbench training is designed in partnership with industry-expert mentors, who teach you through pre-recorded lectures and weekly assignments.

The project-based learning in Advanced Structural Analysis using ANSYS Workbench course curriculum gives you a step-by-step understanding of mechanical APDL solver simulations, ANSYS GUI, ANSYS tools, engineering data, ANSYS SpaceClaim, static structural analysis, ANSYS mechanical modeller, explicit dynamics analysis, and transient structural analysis.

Moreover, the Advanced Structural Analysis using ANSYS Workbench curriculum provides you with in-depth knowledge of explicit and implicit solver operations. Candidates will gain expertise in the critical ANSYS and FEA tools to strengthen your resume for scholarships and grants. Upon satisfactory completion, you will also receive a certification.

8 Weeks

₹ 7,000

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Skills Covered:

Knowledge of engineering

Offered by

Princeton University, Princeton via Edx

Certificate

The Art of Structural Engineering Bridges

Bridges have always played a significant role in infrastructure. However, structural engineering and bridge design are yet to be fully considered from an artistic perspective. Therefore, The Art of Structural Engineering by Edx will help you understand engineering from a creative discipline and art’s point of view.

Furthermore, The Art of Structural Engineering certification syllabus will focus on learning through some of the significant bridges and their examples, built during the industrial revolution. It also deep dives into the social and economic context of bridge design, especially touching upon the interplay between its form and forces. This introductory course includes basic mathematics which is easy to grasp and understand.

Offered by the prestigious Princeton University through Edx, The Art of Structural Engineering online course’s educator will be Maria Garlock, the Civil and Environmental Engineering department’s Professor. The program is engaging, containing a sophisticated methodology that combines engineering and artistic elements in a subtle and well-organized manner.

8 Weeks

Beginner

Compare

Skills Covered:

Civil Engineering skills

Offered by

Penn via Coursera

Certificate

An Introduction to American Law

An Introduction to American Law course is a 11 hours program offered by the University of Pennsylvania via Coursera. The course introduces various areas of American law which includes criminal law, contract law, civil procedure, constitutional law and tort law. The course provides an overview of dilemmas and complexities of the law applications in different aspects from an American point of view.

An Introduction to American Law syllabus covers tort law to sue anyone if other people cause harm and injury to them. The course provides a deep understanding of contract law to monitor the promise between two individuals and the consequences of breaking the promise with various real-life examples.

An Introduction to American Law training explores property law and constitutional law to study the functioning and structure of the United States government with different individual rights. The course focuses on criminal law by discussing punishments and defences used in criminal charges with various excuses and justifications. The course syllabus also includes the civil procedure that should be followed by parties and judges in civil cases.

8 Weeks

Beginner

₹ Free

Compare

Skills Covered:

Legal Knowledge Knowledge of International law

Offered by

KU Leuven, Leuven via Edx

Certificate

Rule of Law and Democracy in Europe

The Rule of Law and Democracy in Europe programme is an interdisciplinary MOOC that discusses the European Union's fundamental principles, shortcomings of the rule of law, and what democracy means in the EU. The course will introduce you to the European Union (EU) and explain its evolution. It attempts to shed light on the values of democracy and the challenges related to it.

The Rule of Law and Democracy in Europe online course will run for an estimated eight weeks. It is designed as a self-paced learning programme. The curriculum consists of videos that test your understanding and knowledge of the topics. You will also learn through testimonials, reflection questions, discussions, and assignments for maximum comprehension.

Additionally, you can choose the verified certificate track to obtain the Rule of Law and Democracy in Europe certificate. Along with the certificate that can be shared on digital platforms, you will also get access to graded assignments, feedback, and instructor support in this mode. Except for the unlimited access and certification of completion, the candidates can even opt for the audit track that is completely free of cost.

8 Weeks

Beginner

Compare

Skills Covered:

Knowledge of law

Offered by

IGNOU via Swayam

Certificate

BGS-011: Understanding Gender and Law

For the BGS-011: Understanding Gender and Law Certification course, Swayam offers an 8-week online program. Dr. Smita M. Patil and Dr. Gurmeet Kaur are the instructors of the course curriculum which investigates the nature of law and its construction within sociopolitical groupings. This course elaborates on how the law is performed and evaluated in the Indian context.

BGS-011: Understanding Gender and Law training is covered in the multidisciplinary curriculum. The course’s syllabus and certificate issuing are the responsibility of the Indira Gandhi National Open University (IGNOU), New Delhi.

BGS-011: Understanding Gender and Law Certification by Swayam expose learners to crucial discussions about gender and law. It addresses vital premises concerning the formation of identities and social spaces, gender, and various sexual identities in the context of women and minority groups.

8 Weeks

Compare

8 Weeks

₹ Free

Compare

Skills Covered:

Manufacturing knowledge

Offered by

MIT Cambridge via Edx

Certificate

Manufacturing Process Control II

The Manufacturing Process Control II certification by the Massachusetts Institute of Technology, Cambridge is an 8-week online course. This online certification course is offered by edX and is part of the Manufacturing MicroMasters program. The Manufacturing Process Control II online course emphasises the foundations of statistical process control to add process modelling and optimisation. In this online certification course from MIT via edX, learners will understand how to design experiments for process improvement and methods to optimise processes and accomplish robustness to noise inputs.

The Manufacturing Process Control II certification syllabus is designed in a way that helps students develop skills in engineering and management essential for competence and competitiveness in the modern manufacturing industry. The curriculum will conclude with a capstone activity that integrates all the Statistical Process Control topics. Participants can attend the Manufacturing Process Control II classes through video lectures by subject matter experts from MIT and graded assignments. Participants will be able to either enrol in the free audit track that has limited access or if they want lifetime access can look to upgrade to the paid verified track so that they do not find any interruption.

8 Weeks

₹ Free

Compare

Skills Covered:

Manufacturing knowledge

Offered by

The Hong Kong Polytechnic University, Hong Kong via Edx

Certificate

Certification Course on Managing Marketing in the Hospitality and Tourism Industry

Managing Marketing in the Hospitality and Tourism Industry course is specially formulated for candidates who want to receive a professional certificate in the tourism and hospitality sector. During the Managing Marketing in the Hospitality and Tourism Industry training creative approaches, such as assignments and projects will be incorporated so that they are exposed to an advanced level of learning. Best practices and communication skills will be taught to the participants so that they learn more efficiently. The applicants will be learning to build customer loyalty and create a strong customer-client relationship.

The Certification Course on Managing Marketing in the Hospitality and Tourism Industry by edX will continue over a course of eight weeks during which the students will be provided with assignments to solve. The program also has the provision of upgrading Managing Marketing in the Hospitality and Tourism Industry training for accessing better learning facilities. The latest key principles that are related to marketing and the theories that are related to the hospitality domain are incorporated in the curriculum of the Certification Course on Managing Marketing in the Hospitality and Tourism Industry by edX.

EdX provides two different options for this online course; verified and audit. In the verified mode, the learners will get unlimited access to the course and a certificate of completion whereas in the free audit mode, they will have a limited duration of access.

8 Weeks

Compare

Skills Covered:

Hospitality skills Knowledge of tourism

Offered by

Stanford via Edx

Certificate

Convex Optimization

The Convex Optimization program will prove beneficial for students or professionals in electrical, mechanical, or civil engineering, computer science, scientific computing, Aero and Astro, operations research, and computational mathematics. This advanced-level course is excellent in learning how to solve application-oriented problems in the field of Convex Optimisation.

The Convex Optimization by edX covers a wide range of topics including, convex analysis, convex sets, linear and quadratic problems, duality theory, minimax, interior-point methods, statistics and machine learning, finance, digital and analog circuits. The course will benefit candidates looking to pursue a career in computer applications or machine learning.

The renowned Stanford University offers the eight-week Convex Optimization online course. There are video lectures in English and transcripts (also in English) to help you follow along. The course instructors, namely Stephen Boyd and Henryk Blasinski, are highly experienced in computer science, mathematical engineering, and other relevant disciplines. Several Ph.D. candidates will also mentor you as additional instructors.

8 Weeks

Expert

Compare

Skills Covered:

Statistical skills Knowledge of engineering

Offered by

Delft University of Technology via Edx

Certificate

Pre-University Calculus

Mathematics is the language of Technology, Engineering, and Science. Calculus is a rudimentary mathematical topic in any engineering or science-based program. That’s why, to prepare you for the introductory calculus courses, edX has designed the Pre-University Calculus training. The program provides a refresher in five essential topics: differentiation, functions, integration, equations, and analytic geometry.

The self-paced Pre-University Calculus program features seven modules and one final exam. The modules themselves have short three-five minute videos in engineering, science, and technology. Moreover, you also get to test your knowledge by tackling interactive exercises and weekly homework. When you’re done with the curriculum, you’ll feel a lot more confident in negotiating with your first university-level calculus course.

After you’ve completed the Pre-University Calculus Certification syllabus, you will be relatively familiar with basic mathematical concepts and necessary definitions. You get to access the course material such as the videos and exercises for free. However, if you wish to have access to the final exam and certificate, you will need to purchase the certificate experience, priced at a nominal fee.

8 Weeks

Beginner

Compare

Skills Covered:

Mathematical skill

Offered by

Doane University, Crete via Edx

Certificate

College Algebra

Becoming a skilled mathematical professional requires immaculate focus and training, but you must also create a strong foundation to handle numerous industry exercises. One of the core areas is Algebra, learning in which you’ll be able to interpret an array of equations and functions, hassle-free. The College Algebra certification course by edX provides a holistic package to this aid, where you’ll become fluent in Algebraic fundamentals.

A Doane University offers the College Algebra certification syllabus that covers critical areas such as inverse functions, graphs, polynomial functions, linear inequalities, exponential functions, equations and their linear systems, and many more. Successful course-takers will become adept in demonstrating increased skills in logical thinking and problem-solving. They will seamlessly pursue further education or employment in this field.

edX believes in furnishing a convenient studying experience and hence, offers the College Algebra online course at entirely no cost. Students will complete the curriculum comfortably in just eight short weeks, dedicating eight to twelve hours per week. Since it is at the intermediate level, learners don’t need to fulfill any eligibility criteria to enroll. The candidates are given the option of two tracks which may be chosen so that the course can be completed. Both the course tracks are self-paced but there is a time limit until which the course remains accessible in the audit mode. But in the case of the verified track, the candidates will be able to access the course materials for an unlimited period of time.

8 Weeks

Intermediate

Compare

Skills Covered:

Mathematical skill

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