RISC International Master's Program in Symbolic Computation and Artificial Intelligence
The combination of symbolic and sub-symbolic methods, often called "hybrid AI", is an upcoming trend in the booming field of artificial intelligence. At RISC, you have the opportunity to earn your master's degree through a combination of existing studies in symbolic computation and machine learning.
Outline of the program
The Master Study "Symbolic Computation and Artificial Intelligence" is pursued in the frame of the existing Master Study "Computational Mathematics" at Johannes Kepler University Linz (JKU). The program utilizes the flexibility offered by the curriculum Computational Mathematics in order to achieve individual study programs aiming at a balanced distribution of courses rooted in symbolic computation and machine learning, respectively. This is accomplished by "importing" necessary and relevant courses from the existing Master Study "Artificial Intelligence" and, to a minimal extent, from the underlying bachelor programs.
General Structure of the Program
The curriculum of the underlying Master "Computational Mathematics" demands a total of 120 ECTS composed of
- 3x12 ECTS from 3 Core Subjects chosen from 9 available Core Subjects,
- 31.5 ECTS freely chosen from 15 available Elective Subjects,
- 12 ECTS of Free Electives without any restrictions, and
- 40.5 ECTS for the Master Thesis (including seminars and an exam).
The curriculum allows to shift up to 6 ECTS from Elective Subjects into Core Subjects (§4 (3)) and to substitute up to 18 ECTS in the Core or Elective Subjects by suitable courses from other curricula (§8). We employ just these two rules to compose a program that is balanced between Symbolic Computation and Machine Learning, details see below.
Target Students
The Master's Program "Symbolic Computation and Artificial Intelligence" addresses in particular
- students holding a bachelor degree in Artificial Intelligence (or related), who are eager to enrich their capabilities with profound mathematics and
- students holding a bachelor degree in Mathematics, who want to broaden their knowledge in the modern area of AI.
See below for details on the individual structure of the program for students with different background and "default paths through the program" depending on different provenience.
Default Path for Students holding a Bachelor Degree in AI from JKU
Students holding a Bachelor Degree in Artificial Intelligence from JKU (033/536) are admitted to the Master Study "Computational Mathematics" (curriculum) without further requirements through §2 (3). Course shifts and substitutions require approval by the Vice Rector for Academic Affairs. The Vice Rector grants the course shifts recommended below (items marked in italics in the course-list below) only if
- the application to the Vice Rector is submitted through the standardized form available at RISC,
- the application to the Vice Rector is signed by the director of RISC, and
- during the bachelor studies, the area of specialization "Mathematics" was chosen (if you chose another area, you may still take part in the program as described under "Paths for Other Students" below)
Furthermore, we recommend to pass some basic mathematics courses (e.g., Algebra and Discrete Mathematics) from the Bachelor Program "Technical Mathematics" under the "Free Electives" during the bachelor studies.
For students holding a bachelor degree in Artificial Intelligence from JKU the Master's Program in Symbolic Computation and Artificial Intelligence has the following structure:
Core Subjects (mandatory, 36 ECTS)
Core Subject 1: Computer Algebra and Number Theory (12 ECTS)
- VL Advanced Computer Algebra
- VL+UE Computer Algebra (4.5 ECTS)1
- VL Symbolic Summation and Integration
Core Subject 2: Symbolic Logic (12 ECTS)
- VL Automated Reasoning
- VL Mathematical Logic
- KV Formal Methods in Software Development
Core Subject 3: Mathematical Methods in Modeling and Data Analysis (12 ECTS)
- VL Machine Learning: Advanced Techniques (3 ECTS)2
- VL Planning and Reasoning in Artificial Intelligence (3 ECTS)2
- VL Deep Learning: Geometric Techniques (3 ECTS)3
- VL Probabilistic Models (3 ECTS)3
Elective Subjects (31.5 ECTS)
Elective Subject 1: Symbolic Computation (15 ECTS)
- Ideally you cover all 15 ECTS from this subject, but you might choose from others.
Elective Subject 2: Mathematical Methods in Engineering (7.5 ECTS)
- Any Master AI (7.5 ECTS)4
Elective Subject 3: Supplementary Subjects (9 ECTS)
- Supplementary AI (9 ECTS)5
Free Electives ...
- ... are free, but can be used to increase the ratio of AI-related courses.
Shifts & Substitutions Explained
- Substitute "VL Number Theory" (4.5 ECTS) by "VL+UE Computer Algebra" (4.5 ECTS) from the curriculum "Bachelor Technical Mathematics (033/201)" (§8).
- Shift these two lectures (VL) from the elective "Supplementary Subjects" in the Master Computational Mathematics to the "Core Subject" (§4 (3)). If you have already done those during your Bachelor's then agree with RISC on two other lectures (VL) from "Supplementary AI" (see the box to the right) with a total volume of 6 ECTS.
- Substitute the remaining 6 ECTS in the Core Subject by these lectures (VL) from the curriculum "Master Artificial Intelligence (066/993)" (§8).
- Substitute 7.5 ECTS in the Elective Subject "Mathematical Methods in Engineering" by any VL/UE/KV/SE from the curriculum "Master Artificial Intelligence (066/993)" (§8).
- Choose any 9 ECTS from "Supplementary AI" that were not yet consumed under 2.
Supplementary AI
With "Supplementary AI" we refer to the following courses from the "Supplementary Subjects" in the "Master Computational Mathematics":
- VL+UE Deep Learning: Architectures and Generative Techniques
- VL+UE Deep Learning: Basic Techniques
- VL+UE LSTM & Transformers
Default Path for Students holding a Bachelor Degree in Mathematics from JKU
Students holding a Bachelor Degree in Technical Mathematics from JKU (033/201) are admitted to the Master Study "Computational Mathematics" (curriculum) without further requirements through §2 (2). Course shifts and substitutions require approval by the Vice Rector for Academic Affairs. The Vice Rector grants the course shifts recommended below (items marked in italics in the course-list below) only if
- the application to the Vice Rector is submitted through the standardized form available at RISC and
- the application to the Vice Rector is signed by the director of RISC.
Furthermore, we recommend to pass some basic AI courses (e.g., Hands-on AI I/II) from the Bachelor Program "Artificial Intelligence" under the "Free Electives" during the bachelor studies.
For students holding a bachelor degree in Mathematics from JKU the Master's Program in Symbolic Computation and Artificial Intelligence has the following structure:
Supplementary AI
With "Supplementary AI" we refer to the following courses from the "Supplementary Subjects" in the "Master Computational Mathematics":
- VL+UE Reinforcement Learning
- VL+UE Deep Learning: Architectures and Generative Techniques
- VL+UE LSTM & Transformers
- VL+UE Machine Learning: Advanced Techniques
Core Subjects (mandatory, 36 ECTS)
Core Subject 1: Computer Algebra and Number Theory (12 ECTS)
- VL Advanced Computer Algebra
- VL+UE Machine Learning: Supervised Techniques (4.5 ECTS)1
- VL Symbolic Summation and Integration
Core Subject 2: Symbolic Logic (12 ECTS)
- VL Automated Reasoning
- VL Mathematical Logic
- KV Formal Methods in Software Development
Core Subject 3: Mathematical Methods in Modeling and Data Analysis (12 ECTS)
- VL Deep Learning: Basic Techniques (3 ECTS)2
- VL Planning and Reasoning in Artificial Intelligence (3 ECTS)2
- VL Deep Learning: Geometric Techniques (3 ECTS)3
- VL Probabilistic Models (3 ECTS)3
Elective Subjects (31.5 ECTS)
Elective Subject 1: Symbolic Computation (15 ECTS)
- Ideally you cover all 15 ECTS from this subject, but you might choose from other electives as well.
Elective Subject 2: Mathematical Methods in Engineering (7.5 ECTS)
- Any Master AI (7.5 ECTS)4
Elective Subject 3: Supplementary Subjects (9 ECTS)
- Supplementary AI (9 ECTS)5
Free Electives ...
- ... are free, but can be used to increase the ratio of AI-related courses.
Shifts & Substitutions Explained
- Substitute "VL Number Theory" (4.5 ECTS) by "VL+UE Machine Learning: Supervised Techniques" (4.5 ECTS) from the curriculum "Bachelor Artificial Intelligence (033/536)" (§8).
- Shift these two lectures (VL) from the elective "Supplementary Subjects" in the Master Computational Mathematics to the "Core Subject" (§4 (3)). If you have already done those during your Bachelor's then agree with RISC on two other lectures (VL) from "Supplementary AI" (see the box to the left) with a total volume of 6 ECTS.
- Substitute the remaining 6 ECTS in the Core Subject by these lectures (VL) from the curriculum "Master Artificial Intelligence (066/993)" (§8).
- Substitute 7.5 ECTS in the Elective Subject "Mathematical Methods in Engineering" by any VL/UE/KV/SE from the curriculum "Master Artificial Intelligence (066/993)" (§8).
- Choose any 9 ECTS from "Supplementary AI" that were not yet consumed under 2 and 3.
A Balanced Education Between Symbolic Computation and Machine Learning
For their Master's Thesis we expect from students in this program to choose a topic related to the combination of symbolic computation and machine learning.
| Bachelor AI | Bachelor Mathematics | |||||
|---|---|---|---|---|---|---|
| SC | ML | Total | SC | ML | ||
| Core Subjects | 24 | 12 | 36 | 19.5 | 16.5 | Core Subjects |
| Elective Subjects | 15 | 16.5 | 31.5 | 15 | 16.5 | Elective Subjects |
| Thesis | 20.25 | 20.25 | 40.5 | 20.25 | 20.25 | Thesis |
| Total | 59.25 | 48.75 | 54.75 | 53.25 | Total | |
Paths for Other Students
Students holding any other Bachelor's degree that fulfills the admission requirements for the Master's Program "Computational Mathematics (066/404)" may use the flexibility of the curriculum and exchange courses as necessary to obtain paths similar to those described above. This is highly individual and depends on the concrete contents of your bachelor studies. Please contact us, we are happy to assist.
Fellowships at the RISC European College
There is a limited number of fellowships available through the RISC European College. Participation in the Master's Program "Computational Mathematics (066/404)" does not require admission to the RISC European College.
Interested to Participate?
Participation in the Master's Program "Symbolic Computation and Artificial Intelligence" formally requires only the admission to the JKU Master's Program "Computational Mathematics".
However, if you are eager to join the program, we recommend a 2-step process.
1. Submit a "Letter of Intent" (LoI) electronically at the following page:
RISC Master's Program Symbolic Computation and Artificial Intelligence
You will have to provide a few details on your prior education, please follow the instructions given on the page. Based on this information we will clarify your individual situation regarding general admission requirements and the shifts and substitutions of courses in the curriculum (see default paths above), which are subject to approval by the Vice Rector of Academic Affairs at JKU. This step results in an agreement on an individual study plan that builds the basis for approval of the requested shifts and substitutions by the Vice Rector of Academic Affairs.
2. Apply for enrollment to the JKU Master's Program "Computational Mathematics" electronically, as described at the following page:
Master's Degree in Computational Mathematics
A study begins in the fall or in the spring semester (October 1 or March 1, respectively). In any case, applications should be sent in timely (several months in advance). Students at Austrian universities may be charged moderate tuition fees. Since these fees depend on citizenship, we refer to above guide for details.
For questions to our program, please contact the RISC Graduate Studies Coordinator.