diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index c53c667f3ef9dbe496f67a7fb15b77151b2e99cd..064060d1b93cc812f0058c4a1ab1f18375aef0d7 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -35,7 +35,7 @@ Documentation:
 Mypy:
   script:
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/prepare-and-run-mypy.sh
-  - ". ./prepare-and-run-mypy.sh python3.6 mypy==0.521 typed-ast==1.0.4"
+  - ". ./prepare-and-run-mypy.sh python3.6 mypy==0.560"
   tags:
   - python3.6
   except:
diff --git a/course/auth.py b/course/auth.py
index 6cfed74bfab4e4db820b0e96d7a9b881446f8011..65212907ed487e50c09587c7d8c579618e34fea2 100644
--- a/course/auth.py
+++ b/course/auth.py
@@ -68,7 +68,7 @@ from relate.utils import StyledForm, StyledModelForm, string_concat, get_site_na
 from django_select2.forms import ModelSelect2Widget
 
 if False:
-    from typing import Any, Text  # noqa
+    from typing import Any, Text, Optional  # noqa
     from django.db.models import query  # noqa
 
 
@@ -1178,6 +1178,7 @@ class APIContext(object):
         self.restrict_to_role = restrict_to_role
 
     def has_permission(self, perm, argument=None):
+        # type: (Text, Optional[Text]) -> bool
         if self.restrict_to_role is None:
             return self.participation.has_permission(perm, argument)
         else:
diff --git a/course/page/text.py b/course/page/text.py
index dc5a5fb27f14bcb8c897e2d1d1a7c9b707de2c81..61fce9365e74d2a49d3c3a6b5106cc52ae76ce52 100644
--- a/course/page/text.py
+++ b/course/page/text.py
@@ -38,6 +38,8 @@ from course.page.base import (
 
         get_editor_interaction_mode)
 
+from typing import cast
+
 import re
 import sys
 
@@ -308,7 +310,7 @@ class RegexMatcher(TextAnswerMatcher):
 
 class CaseSensitiveRegexMatcher(RegexMatcher):
     type = "case_sens_regex"
-    re_flags = 0
+    re_flags = cast(re.RegexFlag, 0)
     is_case_sensitive = True
     pattern_type = "string"
 
diff --git a/run-travis-ci.sh b/run-travis-ci.sh
index f54ca49e611b00e34b1d1962cc99a8fade46e87e..9ae669a0321782448eeb6ebce6d58c6c0c181bf6 100644
--- a/run-travis-ci.sh
+++ b/run-travis-ci.sh
@@ -13,7 +13,7 @@ fi
 if [[ $PY == true ]]; then
   . ./run-tests-for-ci.sh
 elif [[ $Mypy == true ]]; then
-  . ./prepare-and-run-mypy.sh python3.6 mypy==0.521 typed-ast==1.0.4
+  . ./prepare-and-run-mypy.sh python3.6 mypy==0.560
 elif [[ $Flake8 == true ]]; then
   . ./prepare-and-run-flake8.sh relate course accounts tests bin
-fi
\ No newline at end of file
+fi